Absolute Stability and Synchronization in Second-Order Neural Fields with Conduction Delays

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Abstract

We consider a class of neural field models represented by a second-order nonlinear system of integro-differential equations with space-dependent delays. Such a system models interaction of N populations of neurons, each with a continuum description. We justify the existence and uniqueness of solution for the system in a suitable function space. Global existence and boundedness of solutions for the system are confirmed. Two methodologies, the comparison argument and sequential contracting, are developed to establish sufficient conditions for absolute stability and synchronization among different populations of the system. Finally, we present some numerical examples to demonstrate the theoretical results.

Original languageEnglish
Pages (from-to)878-917
Number of pages40
JournalSIAM Journal on Applied Dynamical Systems
Volume22
Issue number2
DOIs
StatePublished - 2023

Keywords

  • absolute stability
  • neural field
  • second-order model
  • synchronization

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