Nonlinear Dynamical Systems

The concepts and techniques developed by mathematicians, physicists, and engineers to characterize and predict the behavior of nonlinear dynamical systems are now being applied to a wide variety of biomedical problems. This chapter serves as an introduction to the central elements of the analysis of nonlinear dynamics systems. The fundamental distinctions between linear and nonlinear systems are described and the basic vocabulary used in studies of nonlinear dynamics introduced. Key concepts are illustrated with classic examples ranging from simple bistability and hysteresis in a damped, driven oscillator to spatiotemporal modes and chaos in large systems, and to multiple attractors in complex Boolean networks. The goal is to give readers less familiar with nonlinear dynamics a conceptual framework for understanding other chapters in this volume.

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