The Study of Complex Systems
What 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:
Agent-based: 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
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.
An Example of a Non-Complex System: This approach contrasts with, say, the neo-classical
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 self-regulation, 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