Spiral attractors as the root of a new type of “bursting activity” in the Rosenzweig–MacArthur model

Bakhanova, Yulia V.; Kazakov, Alexey O.; Korotkov, Alexander G.; Levanova, Tatiana A.; Osipov, Grigory V.

doi:10.1140/epjst/e2018-800025-6

Cited by 18 publications

(12 citation statements)

References 29 publications

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“…However, quasi-in-phase neuron-like regime with quite large interspike intervals can simulate some real processes in neural ensembles [57]. Also, as was shown in [58], such regimes can be both regular and chaotic. In the next section we show that taking into account the coupling through the electromagnetic field based on a memristor give a possibility to control such regimes.…”

Section: Chemical and Electrical Couplings (K 2 = 0)mentioning

confidence: 93%

Effects of memristor-based coupling in the ensemble of FitzHugh–Nagumo elements

Korotkov

Kazakov

Levanova

2019

Eur. Phys. J. Spec. Top.

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In this paper, we study the impact of electrical and memristor-based couplings on some neuron-like spiking regimes, previously observed in the ensemble of two identical FitzHugh-Nagumo elements with chemical excitatory coupling. We demonstrate how increasing strength of these couplings affects on such stable periodic regimes as spiking in-phase, antiphase and sequential activity. We show that the presence of electrical and memristor-based coupling does not essentially affect regimes of in-phase activity. Such regimes do not changes remaining stable ones. However, it is not the case for regimes of anti-phase and sequential activity. All such regimes can transform into periodic or chaotic ones which are very similar to the regimes of in-phase activity. Concerning the regimes of sequential activity, this transformation depends continuously on the coupling parameters, whereas some anti-phase regimes can disappear via a saddle-node bifurcation and nearby orbits tend to regimes of in-phase activity. Also, we show that new interesting neuron-like phenomena can appear from the regimes of sequential activity when increasing the strength of electrical and/or memristor-based coupling. The corresponding regimes can be associated with the appearance of spiral attractors containing a saddle-focus equilibrium with homoclinic orbit and, thus, they correspond to chaotic motions near the invariant manifold of synchronization, which contains all in-phase limit cycles. Such new regimes can lead to the emergence of extreme events in the system of coupled neurons. In particular, the interspike intervals can become arbitrarily large when orbits (corresponding to this regime) pass very close to the saddle-focus. Finally, we show that the 1 arXiv:1903.05472v1 [nlin.CD] further increase in the strength of electrical coupling and/or memristorbased coupling leads to decreasing interspike intervals and, thus, it helps to avoid such extreme behavior.

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Section: Chemical and Electrical Couplings (K 2 = 0)mentioning

confidence: 93%

Effects of memristor-based coupling in the ensemble of FitzHugh–Nagumo elements

Korotkov

Kazakov

Levanova

2019

Eur. Phys. J. Spec. Top.

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“…In order to illustrate it, let us provide the following numerical experiment based on the fact that, when a homoclinic loop exists, the saddle-focus equilibrium becomes part of an attractor, i.e., orbits in the attractor pass arbitrarily close to this equilibrium. Following [10,14], we compute a distance between a sufficiently long orbit in the attractor and the saddle-focus equilibrium. If this distance is less than some small threshold, we assume that a homoclinic orbit exists.…”

Section: One-parameter Bifurcation Analysismentioning

confidence: 99%

On the Organization of Homoclinic Bifurcation Curves in Systems with Shilnikov Spiral Attractors

Bakhanova¹,

Bobrovsky²,

Burdygina³

et al. 2021

Nelin. Dinam.

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We study spiral chaos in the classical Rössler and Arneodo – Coullet – Tresser systems. Special attention is paid to the analysis of bifurcation curves that correspond to the appearance of Shilnikov homoclinic loop of saddle-focus equilibrium states and, as a result, spiral chaos. To visualize the results, we use numerical methods for constructing charts of the maximal Lyapunov exponent and bifurcation diagrams obtained using the MatCont package.

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“…Finally, last three papers investigate ecological systems. Paper [31] reports the emergence of spiral wave chimera patterns in locally coupled ecological network composed of diffusible prey-predator species. Dynamical transitions from spiral wave states to spiral wave chimera followed by incoherent dynamics with respect to increasing diffusion coefficients have been explained as well.…”

Section: The European Physical Journal Special Topicsmentioning

confidence: 99%