What distinguishes CAS from pure SMAs (multi-agent systems) is their focus on high-level and characteristic properties, such as self-similarity, complexity, emergence, and self-organization. An SMA is simply defined as a system composed of multiple interacting agents. In CAS the agents as well as the systems are adaptive, the system is self-similar. A CAS is a complex and self-similar collectivity of adaptive agent interactions. CAS are characterized by a high degree of adaptive capacity, which provides them with resilience "Resilience (ecology)") in the face of disturbance.

Other important properties are adaptation (homeostasis), communication, cooperation, specialization, spatial and temporal organization, and, of course, reproduction. They can organize at all levels: cells specialize, adapt and reproduce themselves just as larger organisms do. Communication and cooperation take place at all levels, from agent to system levels.

Within the class of Complex Systems it is convenient to make a difference between those that are Adaptable and those that are not. According to Axelrod, an Adaptive Complex System is a Complex System made up of agents or populations that seek to adapt through a planned intervention. Under this definition, a tornado is a Non-Adaptive Complex System (the parties do not have the capacity for planned intervention), but pedestrians in a large city make up a Complex Adaptive System (people have the capacity to make planned interventions to avoid colliding with other pedestrians). Axelrod proposes that in a Complex Adaptive System there are three central processes: Variation, Interaction and Selection.

For Mitchell, a Complex (Adaptive) System is “A system in which large networks of components without central control and with simple operating rules give rise to complex collective behavior, sophisticated information processing and adaptation through learning or evolution.” (Mitchell 2009:13). According to Mitchell, this definition contains three common properties of Complex Adaptive Systems:

1. Mitchell shares Holland's idea that complex collective behavior, with changing patterns and difficult to predict, has its origin in collective action rather than in the individual actions of the components of the system.

2. Processing of information and signals produced in both the internal and external environment.

3. Adaptive system changes through learning or evolutionary processes. One of the fundamental authors in the development of the Theory of Complex Adaptive Systems is John H. Holland.

For Holland, a Complex Adaptable System is a system composed of a wide variety of different agents and non-static components that do not maintain a fixed configuration, without a central planning or direction body, but that together develops a unique identity and maintains a stable and coherent pattern over time. In this definition Holland expands the meaning of the term “adaptation” to include learning and the processes related to it.

For Kevin Dooley, a Complex Adaptive System behaves/evolves according to three fundamental principles: the order is emergent rather than having a given level (e.g. neural networks), the history of the system is irreversible and the future of the system is often unpredictable The basic elements of SCA are the agents; which explore their environment and develop schemes for the interpretation and representation of the rules of action. These schemes are subject to change and evolution (Source: K. Dooley, AZ State University).

For Murray Gell-Mann, an Adaptive Complex System acquires information about its environment in which it interacts and identifies regularities in the information obtained, condensing those regularities into a kind of scheme or model and acts in the real world on the basis of that scheme (Source: "The Quark and the Jaguar: Adventures in the Simple and the Complex", p.17).

For Stephanie Forrest, Complex Adaptive Systems are made up of elements that interact and adapt in an operational environment. Agents act and are influenced by their local environment. There is no global control over the system. All agents are only capable of influencing other agents at the local level. Each agent is driven by simple mechanisms, usually condition-action rules, where the conditions are very sensitive to the environment. (Source: Forrest, 1990).

Contenido

Holland menciona cuatro propiedades y tres mecanismos comunes a todos los SCA. Otras propiedades y mecanismos de los Sistemas complejos Adaptables pueden derivarse a partir de estos siete elementos básicos:.

Aggregation

Aggregation can be used in two ways. First, it's an easy way to simplify SCAs by adding similar things into categories. Once an issue of interest is defined, irrelevant details are ignored and things that differ in those details are grouped into a category. Elaborated categories become building blocks that can be combined to build models.

A second use of the aggregation property is related to the emergence of complex behaviors generated by the sum of the interactions of less complex agents. Aggregates (meta-agents) act as agents at a higher level and may exhibit behaviors and adaptive capacity not present in individual agents. In this sense, aggregation provides a hierarchical structure to SCAs.

Non-linearity

Broadly speaking, we can understand linearity as a property that allows us to obtain a value for the whole through a sum of the weighted values ​​of its parts. When a system has the property of linearity, it is easy to use mathematics to create models through trend analysis, sampling methods, or finding equilibrium. Unfortunately SCAs do not have this property of linearity, which makes their study and the establishment of theories particularly difficult. In an SCA, nonlinear interactions almost always cause the aggregate behavior to be more complex than the simple sum of the individual behaviors.

Flows

In SCAs, flows occur from a relationship in the Node-Connector-Resource triad. In general terms, nodes are the agents that carry out resource processing, while connectors are the communication channels that determine possible interactions. In SCAs, flows in the network vary over time as a consequence of the adaptation and learning process. In this process, both nodes and connectors can appear or disappear depending on the success in their search for adaptation. Tags almost always define the main interactions by delimiting the networks and creating the hierarchical structure. Agents with useful tags adapt and spread while those with useless tags eventually become extinct.

Flows have two main properties:

1. The multiplier effect. The effect of an initial action propagates through the network of interactions causing notable changes throughout the system. This effect, which arises regardless of the particular nature of the resource, is evident when evolutionary changes occur.

2. The recycling effect. This effect is due to cycles in the networks. Recycling with the same amount of initial resources can feed the network many times over, causing the system to retain its resources and producing greater resource consumption in each node, which makes the agents prosper to a greater extent.

Diversity

Each agent class occupies a position in the SCA, which is defined by the interactions that center on it. If an agent class is removed, the system will seek to adapt by creating another agent class in the process that provides the missing interactions. In this sense, the persistence of each individual agent depends on the environment, which is largely constituted by other agents. Diversity is also created when a successful agent spreads, generating new opportunities for interaction with other agents. In this process, the opportunity for specialization is also created, which further increases diversity. In a SCA, the interactions disturbed by the extinction of a particular type of agents are commonly reestablished by the appearance of new agents that may be different from the extinct ones, in this way diversity is a product of the continuous adaptations of the SCA.

Labeled

Tagging or labeling is a mechanism “that consistently facilitates the formation of aggregates” (Holland 2004:28), it is the basis of the hierarchical structure present in an SCA. Furthermore, tagging facilitates the selective interaction of an agent with other agents that would be indistinguishable without the use of this mechanism. In this way, tagging constitutes a survival mechanism for aggregation and border formation in SCAs (Holland, 2004). This mechanism allows us to break the symmetries present in a SCA in such a way that we can observe and act on properties that were not evident. Tag-based interactions provide a solid basis for selection, specialization and cooperation.

Internal Models

The learning of agents in an SCA depends on their ability to anticipate and predict the results of their actions. The mechanism of anticipation is the generation of internal models.

The most important characteristic of an internal model is that it must allow useful inferences to be made about the future consequences of the situation being modeled.

The fundamental principle for creating internal models is aggregation into categories. To create an internal model, the agent must select patterns from the information it receives from the environment and generate changes in its internal structure or internal model. Then the changes in the model must allow the agent to anticipate the results that are obtained when the pattern reappears. In higher mammals, internal models depend directly on sensory experience.

In general we will distinguish two classes of internal models:

1. Tacit internal model. It describes a current action motivated by the implicit prediction of some desired future state, as in the case of an amoeba moving in the direction of food.

2. Manifest internal model. It is the basis for explicit, but internal, explorations of the alternatives available to the agent. Both tacit and manifest internal models are present in all SCAs. The evolution process can favor the generation and selection of effective internal models and eliminate inefficient models.

Building Blocks

Internal models are based on limited samples of an environment that is constantly changing. Models will be useful to the extent that we discover certain regularities that are relevant to the situation we wish to model and omit useless details.

Building block search is a reverse capability of aggregation; a complex scene is analyzed trying to identify its component elements that are reusable and have already been tested by natural selection and learning.

Because building models consumes much of the agents' limited resources, then identifying building blocks becomes a critical capability.

The aggregation of building blocks produces building blocks for a higher level, as in the case of quark/nucleon/atom/molecule/organelle/cell...etc.

“We gain experience through repeated use of building blocks, even when they do not appear more than twice in the same situation” (Holland 2004:50) For this reason, when faced with a new situation, we can combine already tested blocks to model the situation, anticipate possible consequences and choose the appropriate action.

When an SCA has tacit internal models, the discovery and combination of building blocks is subject to the time scale determined by the evolution of the system; while if the model is manifest, the time scale is usually of a smaller magnitude.

An important feature of many complex adaptive systems is the emergence of similar global features and structures in completely different systems. Complex adaptive systems are characterized as follows and the most important are:.

• The number of elements is large enough that conventional descriptions (for example, a system of differential equations) are not only impractical, but fail to help in understanding the system, the elements also have to interact and the interaction must be dynamic. Interactions can be physical or involve the exchange of information.

• Such interactions are coarse, that is, any element of the system is affected by and affects other systems.

• The interactions are non-linear which means that small causes can have big results.

• Interactions are mainly but not exclusively with neighboring countries and the nature of influence is modulated.

• Any interaction can feed itself directly or after a series of intermediate stages, such feedback can vary in quality. This is known as “recurrence”.

• Systems are open and it may be difficult or impossible to define the system.

• Complex adaptive systems operate far from equilibrium conditions.

• All complex adaptive systems have a history, they evolve and their past is co-responsible for their present behavior.

• The elements in the system ignore the behavior of the entire system as a whole.

Complex Adaptive Systems can be found in cognitive psychology, artificial intelligence, sociology, ecology, biology, economics and genetics. Below are some examples of SCA with their corresponding agents in parentheses:.

• Markets (merchants).

• Economies (companies).

• Ecosystems (organisms).

• Immune systems (antibodies).

• Biological cells (proteins).

• Social systems (people).

• Political systems (parties).

Another example is the stock market in which adaptive agents (traders) learn day by day and change their actions as they go.

Another good example is the immune system, which starts from the simple, but learns how to prevent complex diseases.

Other examples of SCA include social insects and ant colonies, the biosphere, the ecosystem, the brain, the cell and development of an embryo, manufacturing in business and in general, any social human group, based on culture and a social system such as political parties or social networks of communities.

[1] Holland, John H. (2004). The Hidden Order. Economic Culture Fund.

[2] Holland, John H. (2006). Studying Complex Adaptive Systems, Journal of Systems Science and Complexity 19: http://hdl.handle.net/2027.42/41486.

[3] Axelrod, Robert. (2000). Harnessing Complexity. Basic Books.

[4] Mitchell, Melanie. (2009). Complexity a Guided Tour. Oxford University Press.

[5] Page, Scot E. and Miller, John H. (2007). Complex Adaptive Systems. Princeton University Press.

[6] http://wiki.cas-group.net/index.php?title=Complex_Adaptive_System.

[7] Ozalp Babaoglu, University of Bologna.

[8] Stephanie Forrest, University of New Mexico.

[9] Melanie Mitchell, Portland State University.

[10] Simon A. Levin, Princeton University.

[11] John H. Holland, University of Michigan, Santa Fe Institute.

[12] Murray Gell-Mann, Santa Fe Institute.

[13] Lara Rivero, Arturo (UAM-Xochimilco).

[14] Alvarado López, Raúl (UAM-Xochimilco).

Books

Many of the recent books on complexity and complex adaptive systems have to do with agent-based modeling (ABM) in the social sciences or with the Santa Fe Institute (SFI) and its prestigious researchers: Stuart Kauffman, Murray Gell-Mann, John H. Holland and Chris Langton. The history of the Santa Fe Institute is described by M. Mitchell in his book entitled “Complexity”. Of the many books published by this Institute we have:.

• The Mind, The Brain, and Complex Adaptive Systems, ed. by Harold J. Morowitz, Jerome L. Singer, Santa Fe Institute Studies in the Sciences of Complexity, Addison-Wesley, 1995.

• Introduction to the theory of neural computation, John Hertz, Anders Krogh and Richard Palmer, Santa Fe Institute Studies in the Sciences of Complexity, Addison-Wesley, 1991.

• The Complexity of Cooperation: Agent-Based Models of Competition and Collaboration, Robert Axelrod, Princeton University Press, 1997.

• Emergence: Contemporary Readings in Philosophy and Science, Mark A. Bedau and Paul Humphreys (Eds.), MIT Press, 2007.

• Complexity: Life at the edge of chaos, Roger Lewin, University of Chicago Press, 2000.

• Early Civilizations, Bruce G. Trigger, The American University in Cairo Press, 1993.

• Origins of the modern mind, Merlin Donald, Harvard University Press, 1993.

• The origins of life - from the birth of life to the origins of language, John Maynard Smith and Eörs Szathmáry, Oxford University Press, 1999.

• How Nature works, Per Bak, Springer-Verlag, 1996.

• Complexity and Evolution, Max Pettersson, Cambridge Univ. Press, 1996.

• Generative Social Science: Studies in Agent Based Computational Modeling, Joshua M. Epstein, Princeton University Press, 2007.

• Complex Adaptive Systems: An Introduction to Computational Models of Social Life, John H. Miller & Scott E. Page, Princeton University Press, 2007.

• M. Waldrop, Complexity: The Emerging Science at the Edge of Order and Chaos, Simon & Schuster, 1992.

• Hidden Order: How Adaptation Builds Complexity, John Holland, Basic Books, 1996.

• Emergence: From Chaos To Order, John H. Holland, Basic Books, 1999.

• More books can be found in the following list.

Articles

• John H. Holland, Complex Adaptive Systems: A Primer.

• Ecosystems and the Bioshpere as Complex Adaptive Systems, Simon A. Levin, 1998.

• Complex Adaptive Systems: Exploring the known, the unknown and the unknowable, Simon A. Levin, 2002.

• Gaia as a complex adaptive system, Immune Systems and biological systems (Stephanie Forrest).

• Modeling complex adaptive systems with Echo, S. Forrest and T. Jones. In Complex Systems: Mechanism of Adaptation, R.J. Stonier and X.H. Yu (eds.), Amsterdam, The Netherlands: IOS Press, pp. 3-21 (1994).

• Emergent Computation: Self-organizing, collective, and cooperative phenomena in natural and artificial computing networks, Stephanie Forrest, Physica D 42 (1990) 1-11.

• - Systems engineering.

• - Complex systems.

• - Systems theory.

• - System dynamics.

• - Dynamic system.

• - Complex system.

• - A description Principia Cybernetica Web.

What distinguishes CAS from pure SMAs (multi-agent systems) is their focus on high-level and characteristic properties, such as self-similarity, complexity, emergence, and self-organization. An SMA is simply defined as a system composed of multiple interacting agents. In CAS the agents as well as the systems are adaptive, the system is self-similar. A CAS is a complex and self-similar collectivity of adaptive agent interactions. CAS are characterized by a high degree of adaptive capacity, which provides them with resilience "Resilience (ecology)") in the face of disturbance.

Other important properties are adaptation (homeostasis), communication, cooperation, specialization, spatial and temporal organization, and, of course, reproduction. They can organize at all levels: cells specialize, adapt and reproduce themselves just as larger organisms do. Communication and cooperation take place at all levels, from agent to system levels.

Within the class of Complex Systems it is convenient to make a difference between those that are Adaptable and those that are not. According to Axelrod, an Adaptive Complex System is a Complex System made up of agents or populations that seek to adapt through a planned intervention. Under this definition, a tornado is a Non-Adaptive Complex System (the parties do not have the capacity for planned intervention), but pedestrians in a large city make up a Complex Adaptive System (people have the capacity to make planned interventions to avoid colliding with other pedestrians). Axelrod proposes that in a Complex Adaptive System there are three central processes: Variation, Interaction and Selection.

For Mitchell, a Complex (Adaptive) System is “A system in which large networks of components without central control and with simple operating rules give rise to complex collective behavior, sophisticated information processing and adaptation through learning or evolution.” (Mitchell 2009:13). According to Mitchell, this definition contains three common properties of Complex Adaptive Systems:

1. Mitchell shares Holland's idea that complex collective behavior, with changing patterns and difficult to predict, has its origin in collective action rather than in the individual actions of the components of the system.

2. Processing of information and signals produced in both the internal and external environment.

3. Adaptive system changes through learning or evolutionary processes. One of the fundamental authors in the development of the Theory of Complex Adaptive Systems is John H. Holland.

For Holland, a Complex Adaptable System is a system composed of a wide variety of different agents and non-static components that do not maintain a fixed configuration, without a central planning or direction body, but that together develops a unique identity and maintains a stable and coherent pattern over time. In this definition Holland expands the meaning of the term “adaptation” to include learning and the processes related to it.

For Kevin Dooley, a Complex Adaptive System behaves/evolves according to three fundamental principles: the order is emergent rather than having a given level (e.g. neural networks), the history of the system is irreversible and the future of the system is often unpredictable The basic elements of SCA are the agents; which explore their environment and develop schemes for the interpretation and representation of the rules of action. These schemes are subject to change and evolution (Source: K. Dooley, AZ State University).

For Murray Gell-Mann, an Adaptive Complex System acquires information about its environment in which it interacts and identifies regularities in the information obtained, condensing those regularities into a kind of scheme or model and acts in the real world on the basis of that scheme (Source: "The Quark and the Jaguar: Adventures in the Simple and the Complex", p.17).

For Stephanie Forrest, Complex Adaptive Systems are made up of elements that interact and adapt in an operational environment. Agents act and are influenced by their local environment. There is no global control over the system. All agents are only capable of influencing other agents at the local level. Each agent is driven by simple mechanisms, usually condition-action rules, where the conditions are very sensitive to the environment. (Source: Forrest, 1990).

Contenido

Holland menciona cuatro propiedades y tres mecanismos comunes a todos los SCA. Otras propiedades y mecanismos de los Sistemas complejos Adaptables pueden derivarse a partir de estos siete elementos básicos:.

Aggregation

Aggregation can be used in two ways. First, it's an easy way to simplify SCAs by adding similar things into categories. Once an issue of interest is defined, irrelevant details are ignored and things that differ in those details are grouped into a category. Elaborated categories become building blocks that can be combined to build models.

A second use of the aggregation property is related to the emergence of complex behaviors generated by the sum of the interactions of less complex agents. Aggregates (meta-agents) act as agents at a higher level and may exhibit behaviors and adaptive capacity not present in individual agents. In this sense, aggregation provides a hierarchical structure to SCAs.

Non-linearity

Broadly speaking, we can understand linearity as a property that allows us to obtain a value for the whole through a sum of the weighted values ​​of its parts. When a system has the property of linearity, it is easy to use mathematics to create models through trend analysis, sampling methods, or finding equilibrium. Unfortunately SCAs do not have this property of linearity, which makes their study and the establishment of theories particularly difficult. In an SCA, nonlinear interactions almost always cause the aggregate behavior to be more complex than the simple sum of the individual behaviors.

Flows

In SCAs, flows occur from a relationship in the Node-Connector-Resource triad. In general terms, nodes are the agents that carry out resource processing, while connectors are the communication channels that determine possible interactions. In SCAs, flows in the network vary over time as a consequence of the adaptation and learning process. In this process, both nodes and connectors can appear or disappear depending on the success in their search for adaptation. Tags almost always define the main interactions by delimiting the networks and creating the hierarchical structure. Agents with useful tags adapt and spread while those with useless tags eventually become extinct.

Flows have two main properties:

1. The multiplier effect. The effect of an initial action propagates through the network of interactions causing notable changes throughout the system. This effect, which arises regardless of the particular nature of the resource, is evident when evolutionary changes occur.

2. The recycling effect. This effect is due to cycles in the networks. Recycling with the same amount of initial resources can feed the network many times over, causing the system to retain its resources and producing greater resource consumption in each node, which makes the agents prosper to a greater extent.

Diversity

Each agent class occupies a position in the SCA, which is defined by the interactions that center on it. If an agent class is removed, the system will seek to adapt by creating another agent class in the process that provides the missing interactions. In this sense, the persistence of each individual agent depends on the environment, which is largely constituted by other agents. Diversity is also created when a successful agent spreads, generating new opportunities for interaction with other agents. In this process, the opportunity for specialization is also created, which further increases diversity. In a SCA, the interactions disturbed by the extinction of a particular type of agents are commonly reestablished by the appearance of new agents that may be different from the extinct ones, in this way diversity is a product of the continuous adaptations of the SCA.

Labeled

Tagging or labeling is a mechanism “that consistently facilitates the formation of aggregates” (Holland 2004:28), it is the basis of the hierarchical structure present in an SCA. Furthermore, tagging facilitates the selective interaction of an agent with other agents that would be indistinguishable without the use of this mechanism. In this way, tagging constitutes a survival mechanism for aggregation and border formation in SCAs (Holland, 2004). This mechanism allows us to break the symmetries present in a SCA in such a way that we can observe and act on properties that were not evident. Tag-based interactions provide a solid basis for selection, specialization and cooperation.

Internal Models

The learning of agents in an SCA depends on their ability to anticipate and predict the results of their actions. The mechanism of anticipation is the generation of internal models.

The most important characteristic of an internal model is that it must allow useful inferences to be made about the future consequences of the situation being modeled.

The fundamental principle for creating internal models is aggregation into categories. To create an internal model, the agent must select patterns from the information it receives from the environment and generate changes in its internal structure or internal model. Then the changes in the model must allow the agent to anticipate the results that are obtained when the pattern reappears. In higher mammals, internal models depend directly on sensory experience.

In general we will distinguish two classes of internal models:

1. Tacit internal model. It describes a current action motivated by the implicit prediction of some desired future state, as in the case of an amoeba moving in the direction of food.

2. Manifest internal model. It is the basis for explicit, but internal, explorations of the alternatives available to the agent. Both tacit and manifest internal models are present in all SCAs. The evolution process can favor the generation and selection of effective internal models and eliminate inefficient models.

Building Blocks

Internal models are based on limited samples of an environment that is constantly changing. Models will be useful to the extent that we discover certain regularities that are relevant to the situation we wish to model and omit useless details.

Building block search is a reverse capability of aggregation; a complex scene is analyzed trying to identify its component elements that are reusable and have already been tested by natural selection and learning.

Because building models consumes much of the agents' limited resources, then identifying building blocks becomes a critical capability.

The aggregation of building blocks produces building blocks for a higher level, as in the case of quark/nucleon/atom/molecule/organelle/cell...etc.

“We gain experience through repeated use of building blocks, even when they do not appear more than twice in the same situation” (Holland 2004:50) For this reason, when faced with a new situation, we can combine already tested blocks to model the situation, anticipate possible consequences and choose the appropriate action.

When an SCA has tacit internal models, the discovery and combination of building blocks is subject to the time scale determined by the evolution of the system; while if the model is manifest, the time scale is usually of a smaller magnitude.

An important feature of many complex adaptive systems is the emergence of similar global features and structures in completely different systems. Complex adaptive systems are characterized as follows and the most important are:.

• The number of elements is large enough that conventional descriptions (for example, a system of differential equations) are not only impractical, but fail to help in understanding the system, the elements also have to interact and the interaction must be dynamic. Interactions can be physical or involve the exchange of information.

• Such interactions are coarse, that is, any element of the system is affected by and affects other systems.

• The interactions are non-linear which means that small causes can have big results.

• Interactions are mainly but not exclusively with neighboring countries and the nature of influence is modulated.

• Any interaction can feed itself directly or after a series of intermediate stages, such feedback can vary in quality. This is known as “recurrence”.

• Systems are open and it may be difficult or impossible to define the system.

• Complex adaptive systems operate far from equilibrium conditions.

• All complex adaptive systems have a history, they evolve and their past is co-responsible for their present behavior.

• The elements in the system ignore the behavior of the entire system as a whole.

Complex Adaptive Systems can be found in cognitive psychology, artificial intelligence, sociology, ecology, biology, economics and genetics. Below are some examples of SCA with their corresponding agents in parentheses:.

• Markets (merchants).

• Economies (companies).

• Ecosystems (organisms).

• Immune systems (antibodies).

• Biological cells (proteins).

• Social systems (people).

• Political systems (parties).

Another example is the stock market in which adaptive agents (traders) learn day by day and change their actions as they go.

Another good example is the immune system, which starts from the simple, but learns how to prevent complex diseases.

Other examples of SCA include social insects and ant colonies, the biosphere, the ecosystem, the brain, the cell and development of an embryo, manufacturing in business and in general, any social human group, based on culture and a social system such as political parties or social networks of communities.

[1] Holland, John H. (2004). The Hidden Order. Economic Culture Fund.

[2] Holland, John H. (2006). Studying Complex Adaptive Systems, Journal of Systems Science and Complexity 19: http://hdl.handle.net/2027.42/41486.

[3] Axelrod, Robert. (2000). Harnessing Complexity. Basic Books.

[4] Mitchell, Melanie. (2009). Complexity a Guided Tour. Oxford University Press.

[5] Page, Scot E. and Miller, John H. (2007). Complex Adaptive Systems. Princeton University Press.

[6] http://wiki.cas-group.net/index.php?title=Complex_Adaptive_System.

[7] Ozalp Babaoglu, University of Bologna.

[8] Stephanie Forrest, University of New Mexico.

[9] Melanie Mitchell, Portland State University.

[10] Simon A. Levin, Princeton University.

[11] John H. Holland, University of Michigan, Santa Fe Institute.

[12] Murray Gell-Mann, Santa Fe Institute.

[13] Lara Rivero, Arturo (UAM-Xochimilco).

[14] Alvarado López, Raúl (UAM-Xochimilco).

Books

Many of the recent books on complexity and complex adaptive systems have to do with agent-based modeling (ABM) in the social sciences or with the Santa Fe Institute (SFI) and its prestigious researchers: Stuart Kauffman, Murray Gell-Mann, John H. Holland and Chris Langton. The history of the Santa Fe Institute is described by M. Mitchell in his book entitled “Complexity”. Of the many books published by this Institute we have:.

• The Mind, The Brain, and Complex Adaptive Systems, ed. by Harold J. Morowitz, Jerome L. Singer, Santa Fe Institute Studies in the Sciences of Complexity, Addison-Wesley, 1995.

• Introduction to the theory of neural computation, John Hertz, Anders Krogh and Richard Palmer, Santa Fe Institute Studies in the Sciences of Complexity, Addison-Wesley, 1991.

• The Complexity of Cooperation: Agent-Based Models of Competition and Collaboration, Robert Axelrod, Princeton University Press, 1997.

• Emergence: Contemporary Readings in Philosophy and Science, Mark A. Bedau and Paul Humphreys (Eds.), MIT Press, 2007.

• Complexity: Life at the edge of chaos, Roger Lewin, University of Chicago Press, 2000.

• Early Civilizations, Bruce G. Trigger, The American University in Cairo Press, 1993.

• Origins of the modern mind, Merlin Donald, Harvard University Press, 1993.

• The origins of life - from the birth of life to the origins of language, John Maynard Smith and Eörs Szathmáry, Oxford University Press, 1999.

• How Nature works, Per Bak, Springer-Verlag, 1996.

• Complexity and Evolution, Max Pettersson, Cambridge Univ. Press, 1996.

• Generative Social Science: Studies in Agent Based Computational Modeling, Joshua M. Epstein, Princeton University Press, 2007.

• Complex Adaptive Systems: An Introduction to Computational Models of Social Life, John H. Miller & Scott E. Page, Princeton University Press, 2007.

• M. Waldrop, Complexity: The Emerging Science at the Edge of Order and Chaos, Simon & Schuster, 1992.

• Hidden Order: How Adaptation Builds Complexity, John Holland, Basic Books, 1996.

• Emergence: From Chaos To Order, John H. Holland, Basic Books, 1999.

• More books can be found in the following list.

Articles

• John H. Holland, Complex Adaptive Systems: A Primer.

• Ecosystems and the Bioshpere as Complex Adaptive Systems, Simon A. Levin, 1998.

• Complex Adaptive Systems: Exploring the known, the unknown and the unknowable, Simon A. Levin, 2002.

• Gaia as a complex adaptive system, Immune Systems and biological systems (Stephanie Forrest).

• Modeling complex adaptive systems with Echo, S. Forrest and T. Jones. In Complex Systems: Mechanism of Adaptation, R.J. Stonier and X.H. Yu (eds.), Amsterdam, The Netherlands: IOS Press, pp. 3-21 (1994).

• Emergent Computation: Self-organizing, collective, and cooperative phenomena in natural and artificial computing networks, Stephanie Forrest, Physica D 42 (1990) 1-11.

• - Systems engineering.

• - Complex systems.

• - Systems theory.

• - System dynamics.

• - Dynamic system.

• - Complex system.

• - A description Principia Cybernetica Web.