Synchronized chaos and other coherent states for two coupled neurons

The parametrized time-discrete dynamics of two recurrently coupled chaotic neurons is investigated. Basic dynamical features of this system are demons trated for symmetric couplings of identical neurons. Periodic as well as ch aotic orbits constrained to a manifold M of synchronized states are observe d. Parameter domains for locally stable synchronization manifolds M are det ermined by numerical simulations. In addition to the synchronized dynamics there often co-exist periodic, quasiperiodic and even chaotic attractors re presenting different kinds of non-synchronous coherent dynamics. Simulation results for selected sets of parameters are presented, and synchronization conditions for systems with non-identical neurons are derived. Also these more general systems inherit the above-mentioned dynamical properties. (C) 1999 Elsevier Science B.V.