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

Author

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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)

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.

Suggested Citation

  • Lev Ryashko & Anna Otman & Irina Bashkirtseva, 2025. "Multirhythmicity, Synchronization, and Noise-Induced Dynamic Diversity in a Discrete Population Model with Competition," Mathematics, MDPI, vol. 13(5), pages 1-18, March.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:5:p:857-:d:1605562
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    References listed on IDEAS

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    1. Quan Wang & Li Zu & Daqing Jiang & Donal O’Regan, 2023. "Study on Dynamic Behavior of a Stochastic Predator–Prey System with Beddington–DeAngelis Functional Response and Regime Switching," Mathematics, MDPI, vol. 11(12), pages 1-17, June.
    2. Belyaev, Alexander & Bashkirtseva, Irina & Ryashko, Lev, 2021. "Stochastic variability of regular and chaotic dynamics in 2D metapopulation model," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    3. Oksana Revutskaya & Galina Neverova & Efim Frisman, 2024. "Discrete-Time Model of an Exploited Population with Age and Sex Structures: Instability and the Hydra Effect," Mathematics, MDPI, vol. 12(4), pages 1-27, February.
    4. Nirapada Santra & Sudeshna Mondal & Guruprasad Samanta, 2022. "Complex Dynamics of a Predator–Prey Interaction with Fear Effect in Deterministic and Fluctuating Environments," Mathematics, MDPI, vol. 10(20), pages 1-38, October.
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