Existence of physical measures in some excitation-inhibition networks

Matteo Tanzi, Lai Sang Young

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Article numberA8
Issue number2
StatePublished - Feb 2022


  • SRB measures
  • coupled dynamical systems
  • smooth ergodic theory

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • General Physics and Astronomy
  • Applied Mathematics


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