Collective chaos in pulse-coupled neural networks

¹ CNR - Consiglio Nazionale delle Ricerche, Istituto dei Sistemi Complessi - via Madonna del Piano 10, I-50019 Sesto Fiorentino, Italy, EU
² INFN Sezione Firenze - via Sansone, 1, I-50019 Sesto Fiorentino, Italy, EU
³ Centro Interdipartimentale per lo Studio delle Dinamiche Complesse - via Sansone, 1, I-50019 Sesto Fiorentino, Italy, EU

^a alessandro.torcini@cnr.it

Received: 14 October 2010
Accepted: 7 December 2010

Abstract

We study the dynamics of two symmetrically coupled populations of identical leaky integrate-and-fire neurons characterized by an excitatory coupling. Upon varying the coupling strength, we find symmetry-breaking transitions that lead to the onset of various chimera states as well as to a new regime, where the two populations are characterized by a different degree of synchronization. Symmetric collective states of increasing dynamical complexity are also observed. The computation of the the finite-amplitude Lyapunov exponent allows us to establish the chaoticity of the (collective) dynamics in a finite region of the phase plane. The further numerical study of the standard Lyapunov spectrum reveals the presence of several positive exponents, indicating that the microscopic dynamics is high-dimensional.