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

• Published in: Communications in nonlinear science & numerical simulation Vol. 95; p. 105611
• Main Authors: Bashkirtseva, Irina, Ryashko, Lev, Pisarchik, Alexander N.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.04.2021; Elsevier Science Ltd
• Subjects: Bifurcations; Chaos; Chaos theory; Mathematical models; Neural model; Noise; Nonlinear systems; Oscillators; Phase transitions; Stochastic bifurcations; Stochastic models; Stochastic sensitivity; Stochastic systems; Synchronism; Synchronization; Chaos; Stochastic sensitivity; Synchronization; Noise; Stochastic bifurcations; Neural model
• ISSN: 1007-5704; 1878-7274
• DOI: 10.1016/j.cnsns.2020.105611

•Oscillatory behavior in coupled map-based neural oscillators is studied.•We analyze noise-induced transitions between in-phase and anti-phase dynamics.•We apply an analytical approach based on the stochastic sensitivity functions.•Coupling-induced stochastic order-chaos transformations are discussed. 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.