The Ricker Competition Model of Two Species: Dynamic Modes and Phase Multistability

Matvey Kulakov, Galina Neverova and Efim Frisman
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Matvey Kulakov: Institute for Complex Analysis of Regional Problems, Far Eastern Branch, Russian Academy of Sciences, 679016 Birobidzhan, Russia
Galina Neverova: Institute of Automation and Control Processes, Far Eastern Branch, Russian Academy of Sciences, 690041 Vladivostok, Russia
Efim Frisman: Institute for Complex Analysis of Regional Problems, Far Eastern Branch, Russian Academy of Sciences, 679016 Birobidzhan, Russia

Mathematics, 2022, vol. 10, issue 7, 1-23

Abstract: The model of two species competing for a resource proposed by R. May and A.P. Shapiro has not yet been fully explored. We study its dynamic modes. The model reveals complex dynamics: multistable in-phase and out-of-phase cycles, and their bifurcations occur. The multistable out-of-phase dynamic modes can bifurcate via the Neimark–Sacker scenario. A value variation of interspecific competition coefficients changes the number of in-phase and out-of-phase modes. We have suggested an approach to identify the bifurcation (period-doubling, pitchfork, or saddle-node bifurcations) due to which in-phase and out-of-phase periodic points appear. With strong interspecific competition, the population’s survival depends on its growth rate. However, with a specific initial condition, a species with a lower birth rate can displace its competitor with a higher one. With weak interspecific competition and sufficiently high population growth rates, the species coexist. At the same time, the observed dynamic mode or the oscillation phase can change due to altering of the initial condition values. The influence of external factors can be considered as an initial condition modification, leading to dynamics shift due to the coexistence of several stable attractors.

Keywords: periodic fixed points; bifurcation; synchronization; multistability; chaos; community development scenario; competing populations; dynamic mode change (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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