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Stochastic phenomena in the system of coupled populations

Belyaev A.V., Ryashko L.B.

Ural Mathematical Center, Ural Federal University, Russia, 620083, Ekaterinburg, Lenina 51

In this paper, we consider a metapopulation consisting of two coupled populations modeled by the Ricker map. The aim of this research is to analyze the dynamic modes of corporate dynamics with variations in the intensity of coupling [1] and random disturbances. Isolated subsystems, that is, those in which the coupling coefficient is zero, can be in various stable modes: equilibrium, oscillatory, and chaotic. Namely, in this case, systems are considered in equilibrium modes. If maps are coupled, the behavior of the system can change significantly, for example, the equilibrium regime transforms into a periodic, quasi-periodic, and chaotic regime, and the chaotic regime again into a regular one. In this paper, a parametric study of possible scenarios for changing corporate dynamics and their connection with bifurcations of different types is carried out. The attractors of the system are constructed and studied, and the analysis of time series of coordinates is made. A stochastic system is considered that takes into account the random impact on the metapopulation. Using the stochastic sensitivity sensitivity function technique and the method of confidence domains, such stochastic phenomena as the stabilization of an unstable equilibrium, the extinction of the population with a change in the intensity of noise, and the appearance of noise-induced chaos are investigated and demonstrated.

References 1. Bashkirtseva I., Pisarchik A. Variability and effect of noise on the corporate dynamics of coupled oscillators // AIP Conference Proceedings Vol. 2172, No. 070004, Year 2019.

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