Author:
Tanzi Matteo,Young Lai-Sang
Abstract
Abstract
In this paper we present a rigorous analysis of a class of coupled dynamical systems in which two distinct types of components, one excitatory and the other inhibitory, interact with one another. These network models are finite in size but can be arbitrarily large. They are inspired by real biological networks, and possess features that are idealizations of those in biological systems. Individual components of the network are represented by simple, much studied dynamical systems. Complex dynamical patterns on the network level emerge as a result of the coupling among its constituent subsystems. Appealing to existing techniques in (nonuniform) hyperbolic theory, we study their Lyapunov exponents and entropy, and prove that large time network dynamics are governed by physical measures with the SRB property.
Funder
Division of Mathematical Sciences
H2020 Marie Skłodowska-Curie Actions
Subject
Applied Mathematics,General Physics and Astronomy,Mathematical Physics,Statistical and Nonlinear Physics
Cited by
2 articles.
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1. Random‐like properties of chaotic forcing;Journal of the London Mathematical Society;2022-06-24
2. Stability of heteroclinic cycles in ring graphs;Chaos: An Interdisciplinary Journal of Nonlinear Science;2022-06