Multirhythmicity, Synchronization, and Noise-Induced Dynamic Diversity in a Discrete Population Model with Competition

Lev Ryashko (), Anna Otman and Irina Bashkirtseva
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Lev Ryashko: Institute of Natural Sciences and Mathematics, Ural Federal University, Lenina 51, 620000 Ekaterinburg, Russia
Anna Otman: Institute of Natural Sciences and Mathematics, Ural Federal University, Lenina 51, 620000 Ekaterinburg, Russia
Irina Bashkirtseva: Institute of Natural Sciences and Mathematics, Ural Federal University, Lenina 51, 620000 Ekaterinburg, Russia

Mathematics, 2025, vol. 13, issue 5, 1-18

Abstract: The problem of mathematical modeling and analysis of stochastic phenomena in population systems with competition is considered. This problem is investigated based on a discrete system of two populations modeled by the Ricker map. We study the dependence of the joint dynamic behavior on the parameters of the growth rate and competition intensity. It is shown that, due to multistability, random perturbations can transfer the population system from one attractor to another, generating stochastic P -bifurcations and transformations of synchronization modes. The effectiveness of a mathematical approach, based on the stochastic sensitivity technique and the confidence domain method, in the parametric analysis of these stochastic effects is demonstrated. For monostability zones, the phenomenon of stochastic generation of the phantom attractor is found, in which the system enters the trigger mode with alternating transitions between states of almost complete extinction of one or the other population. It is shown that the noise-induced effects are accompanied by stochastic D -bifurcations with transitions from order to chaos.

Keywords: mathematical modeling; population dynamics; competition; stochastic sensitivity; confidence domain; synchronization; chaos (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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