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About the Science of Complexity

We consider a system "complex" if it is composed of diverse components that interact in interesting (nonlinear) ways, for example:

• voters and politicians in an election
• consumers and firms in an economy
• vehicles in transportation systems
• cells and microbes in a body
• flora and fauna in an ecosystem
• disease, culture and technology spread in a society
• information over a social or computer network

In a complex systems model, one usually makes assumptions about the characteristics of and interactions between the individual components or "agents" of the system and analyzes the model to understand what properties and activities of the total system emerge from these assumptions.

In a complex system the agents are usually numerous, diverse and dynamic. They are intelligent but not perfect decision-makers. They learn and adapt in response to feedback from their activities. They interact in structured ways, often forming organizations to carry out their tasks. They operate in a dynamic world that is rarely in equilibrium and often in chaos. To emphasize the learning and adaptation that occur in these dynamic worlds, we often call these systems "complex adaptive systems."

In a non-complex system, the agents are usually few or infinite in number, they are often identical to each other and perfectly rational. Their encounters are random and their world is a static one in complete equilibrium. Prior to the complex systems approach, these assumptions were thought to be necessary to enable formal analysis. Complex systems theory shows that these strong assumptions can be relaxed with the result being a richer, more diverse and dynamic set of theories.

Often, attributes of complex systems models in one field, such as ecology, have much in common with characteristics of other fields, such as immunology or economics. As a result, the complex systems approach is inherently interdisciplinary; insights and results can be translated across fields.

Characteristics of Complex Systems:

Agent-based: the basic building blocks are the individual agents of the system.

Heterogeneous: the agents differ in important characteristics.

Dynamic: the agents change over time. The dynamics that describe how the system changes over time are usually nonlinear, sometimes even chaotic. The system is rarely in any long run equilibrium.

Feedback: These changes are often the result of feedback that the agents receive as a result of their activities.

Organization: agents are organized into groups or hierarchies. These organizations are often rather structured, and these structures influence how the underlying system evolves over time.

Emergence: the overlying concerns in these models are the macro-level behaviors that emerge from the assumptions about the actions and interactions of the individual agents.

Computer Simulations: often a key component of the study of complex systems. In many cases, computer simulations are outgrowths or natural extensions of the insights of simpler mathematical models. In other cases, computer simulations are constructed by modeling directly the (greatly simplified) features and interactions of the agents in the system being modeled.

Interdisciplinary Approach: an important aspect of the complex systems approach is the recognition that many different kinds of systems include self-regulation, feedback or adaptation in their dynamics and thus may have a common underlying structure despite their apparent differences.

Mathematical Techniques: the mathematical techniques of the complex systems approach include: nonlinear dynamics, especially differential equations, difference equations and cellular automata, game theory, Markov processes, genetic algorithms, graph theory and time series analysis.

Examples: Here are a few examples of complex systems models in the social, life and decision sciences.

Updated September 1, 2005