Stochastic analysis of dynamic transformations in a system of migration-coupled chaotic populations with the Allee effect

Abstract

The problem of identifying mechanisms of abrupt changes in the dynamics of coupled stochastic systems is investigated. This problem is studied for a metapopulation consisting of two functionally coupled chaotic subsystems modeled by the Ricker map with Allee effect. For the initial deterministic model, a variety of dynamical modes with chaos-order transformations, different regimes of synchronization and transitions to extinction is parametrically investigated in dependence of migration intensity. We perform an extended analysis of stochastic phenomena caused by random fluctuations in the intensity of coupling: (i) noise-induced order-chaos transformations; (ii) stochastic transitions between attractors with suppression of periodic oscillations; (iii) noise-induced extinction of metapopulation. To analyze all these stochastic effects, we use both statistical processing of numerical simulation results and a new mathematical technique using stochastic sensitivity functions and confidence domains.