Dynamical Systems: Overview
Many models of computational neuroscience are formulated in terms of nonlinear dynamical system (sometimes the dynamical system with noise) and include a large number of parameters. Therefore, it is difficult to analyze dynamics and find correspondence between parameter values and dynamical mode. Mathematical theory of dynamical systems and bifurcations provide a valuable tool for a qualitative study and finding regions in parameter space corresponding to different dynamical modes (e.g., oscillations or bistability). Thus, the dynamical systems (or nonlinear dynamics) approach to analysis of neural systems has played a central role for computational neuroscience for many years (summarized, e.g., in recent textbooks, Izhikevich (2007) and Ermentrout and Terman (2010)).
Theory of dynamical systems and bifurcations provides a list of universal scenarios of dynamics changes under parameter variation. For example, one scenario explaining the onset of...
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