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The Study of Complex SystemsWhat is the Study of Complex Systems?In everyday conversation, we call a system "complex" if it has many components that interact in an interesting way. More formally, we consider a phenomenon in the social, life, physical or decision sciences a complex system if it has a significant number of the following characteristics: Agentbased: The basic building blocks are the characteristics and activities of the individual agents in the environment under study. Heterogeneous: These agents differ in important characteristics. Dynamic: These characteristics that change over time, as the agents adapt to their environment, learn from their experiences, or experience natural selection in the regeneration process. 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 macrolevel behaviors that emerge from the assumptions about the actions and interactions of the individual agents. An Example of a NonComplex System: This approach contrasts with, say, the neoclassical approach to modeling economic systems. Usually, in order to work with expressions and equations that are tractable by mathematical analysis, microeconomic theorists assume that all consumers are identical and never change their preferences or characteristics. (so much for education or advertising!) Consumers either do not communicate at all or they interact in some simplistic random fashion, and the underlying system is always in equilibrium. Rarely do macroeconomic models build naturally on the underlying microeconomic models, as the complex systems approach strives to do. Frontier Between Simplicity and Complexity: Because of their simplifying assumptions, classical economics theorists can often use mathematical analysis to derive the basic properties of the system they are studying. Any inclusion of heterogeneity, organization, or adaptation would require the use of computer simulation or of numerical analysis to understand how the more realistic system works. Many feel that this threshold between overly simple, but mathematically tractable, models and models that require computer simulation is exactly where the complex systems approach thrives. In any case, computer simulations play a central role in complex systems analysis. Computer Simulations: 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. Then, analysis of the dynamics and emergent behavior of these simulation models can lead to new mathematical models, new hypotheses and new real world experiments or field studies to test these new models and hypotheses. Interdisciplinary Approach: An important aspect of the complex systems approach is the recognition that many different kinds of systems include selfregulation, feedback or adaptation in their dynamics and thus may have a common underlying structure despite their apparent differences. These deep structural similarities can often be exploited to transfer methods of analysis and understanding from one field to another. In addition to developing deeper understandings of specific systems, such interdisciplinary approaches should help elucidate the general structure and behavior of complex systems, and move us toward a deeper appreciation of the general nature of such systems. Examples: Press Here for few examples of complex systems models in the social, life and decision sciences. Mathematical Techniques: The mathematical techniques of the complex system approach include: nonlinear dynamics, especially differential equations, difference equations and cellular automata, game theory, Markov processes, genetic algorithms, graph theory and time series analysis. 
