ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)


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Kurilova E. V., Kulakov M. P., Frisman E. Y. Mechanisms leading to bursting oscillations in the system of predator–prey communities coupled by migrations. Izvestiya VUZ. Applied Nonlinear Dynamics, 2023, vol. 31, iss. 2, pp. 143-169. DOI: 10.18500/0869-6632-003030, EDN: FGDHHM

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Russian
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Mechanisms leading to bursting oscillations in the system of predator–prey communities coupled by migrations

Autors: 
Kurilova Ekaterina Viktorovna, Institute for Complex Analysis of Regional Problems of Russian Academy of Sciences, Far Eastern Branch
Kulakov Matvej Pavlovich, Institute for Complex Analysis of Regional Problems of Russian Academy of Sciences, Far Eastern Branch
Frisman Efim Yakovlevich, Institute for Complex Analysis of Regional Problems of Russian Academy of Sciences, Far Eastern Branch
Abstract: 

The purpose is to study the periodic regimes of the dynamics for two non-identical predator–prey communities coupled by migrations, associated with the partial synchronization of fluctuations in the abundance of communities. The combination of fluctuations in neighboring sites leads to the regimes that include both fast bursts (bursting oscillations) and slow oscillations (tonic spiking). These types of activity are characterized by a different ratio of synchronous and non-synchronous dynamics of communities in certain periods of time. In this paper, we describe scenarios of the transition between different types of burst activity. These types of dynamics differ from each other not so much in size, shape, and number of spikes in a burst, but in the order of these bursts relative to the slow-fast cycle.

Methods. To study the proposed model, we use the bifurcation analysis methods of dynamic systems, as well as geometric methods based on the division of the full system into fast and slow equations (subsystems).

Results. We showed that the dynamics of the first subsystem with a slow-fast limit cycle directly determines the dynamics of the second one with burst activity through a smooth dependence of regime on the number of predators and a non-smooth dependence on the number of prey. We constructed the invariant manifolds on which there are parts of dynamics with tonic (slow manifold) and burst (fast manifold) activity of the full system.

Conclusion. We described the scenario for bursting with different waveforms, which are determined by the appearance of the fast invariant manifold and the location of its parts relative to the slow-fast cycle. The transitions between different types of burst are accompanied by a change in the oscillation period, the degree of synchronization, and, as a result, the dynamics becomes quasi-periodic when both communities are not synchronous with each other.

Acknowledgments: 
This work was carried out within the framework of the state targets of the Institute for Complex Analysis of Regional Problem of the Far Eastern Branch of the Russian Academy of Sciences
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Received: 
22.09.2022
Accepted: 
26.12.2022
Available online: 
27.02.2023
Published: 
31.03.2023