Stochastic transitions between in-phase and anti-phase synchronization in coupled map-based neural oscillators

A problem of mathematical modeling and analysis of complex oscillatory behavior in coupled nonlinear stochastic systems is considered. We study stochastic bifurcations and transitions between in-phase and anti-phase dynamics in two coupled map-based neural oscillators with regular and chaotic attractors. Interesting dynamical regimes of isolated and coupled oscillators are considered in a wide range of both deterministic and stochastic modes associated with in-phase and anti-phase synchronization. The comprehensive nonlinear and stochastic analyses using a stochastic sensitivity approach and confidence ellipses allowed us to reveal the geometry of multiple basins of attraction of coexisting states and confidence areas in both synchronous and asynchronous regimes. Coupling-induced and noise-induced transitions between order and chaos are also discussed. (C) 2020 Elsevier B.V. All rights reserved.