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Introduction to the Modeling and Analysis of Complex Systems introduces students to mathematical/computational modeling and analysis developed in the emerging interdisciplinary field of Complex Systems Science. Complex systems are systems made of a large number of microscopic components interacting with each other in nontrivial ways.

• ## 3: Basics of Dynamical Systems

A dynamical system is a system whose state is uniquely speci&filig;ed by a set of variables and whose behavior is described by prede&filig;ned rules.
• ## 4: Discrete-Time Models I - Modeling

Discrete-time models are easy to understand, develop and simulate. They are easily implementable for stepwise computer simulations, and they are often suitable for modeling experimental data that are almost always already discrete. Moreover, they can represent abrupt changes in the system’s states, and possibly chaotic dynamics, using fewer variables than their continuous-time counterparts.