35 citations · 170 across the 18 of their papers we have counts for
18 papers
Heteroclinic cycles and chaos in a system of four identical phase oscillators with global biharmonic coupling
Aleksei M. Arefev, Evgeny A. Grines, Grigory V. Osipov
We study a system of four identical globally coupled phase oscillators with biharmonic coupling function. Its dimension and the type of coupling make it the minimal system of Kuram…
Cyclops states in repulsive Kuramoto networks: the role of higher-order coupling
V. O. Munyayev, M. I. Bolotov, L. A. Smirnov +2
Repulsive oscillator networks can exhibit multiple cooperative rhythms, including chimera and cluster splay states. Yet, understanding which rhythm prevails remains challenging. He…
Stability of rotatory solitary states in Kuramoto networks with inertia
V. O. Munyaev, M. I. Bolotov, L. A. Smirnov +2
Solitary states emerge in oscillator networks when one oscillator separates from the fully synchronized cluster and becomes incoherent with the rest of the network. Such chimera-ty…
Finite-density-induced motility and turbulence of chimera solitons
L. A. Smirnov, M. I. Bolotov, D. I. Bolotov +2
We consider a one-dimensional oscillatory medium with a coupling through a diffusive linear field. In the limit of fast diffusion this setup reduces to the classical Kuramoto-Batto…
Disorder fosters chimera in an array of motile particles
L. A. Smirnov, M. I. Bolotov, G. V. Osipov +1
We consider an array of non-locally coupled oscillators on a ring, which for equally spaced units possesses a Kuramoto-Battogtokh chimera regime and a synchronous state. We demonst…
Appearance of chaos and hyperchaos in evolving pendulum network
V. O. Munyaev, D. S. Khorkin, M. I. Bolotov +2
The study of deterministic chaos continues to be one of the important problems in the field of nonlinear dynamics. Interest in the study of chaos exists both in low-dimensional dyn…
Synchronization structures in the chain of rotating pendulums
V. O. Munyaev, D. S. Khorkin, M. I. Bolotov +2
The collective behavior of the ensembles of coupled nonlinear oscillator is one of the most interesting and important problems in modern nonlinear dynamics. In this paper, we study…
Dynamics in a phase model of half-center oscillator: two neurons with excitatory coupling
A. G. Korotkov, T. A. Levanova, M. A. Zaks +1
A minimalistic model of the half-center oscillator is proposed. Within it, we consider dynamics of two excitable neurons interacting by means of the excitatory coupling. In the par…
Describing dynamics of driven multistable oscillators with phase transfer curves
Evgeny Grines, Grigory Osipov, Arkady Pikovsky
Phase response curve is an important tool in studies of stable self-sustained oscillations; it describes a phase shift under action of an external perturbation. We consider multist…
Variety of rotation modes in a small chain of coupled pendulums
M. I. Bolotov, V. O. Munyaev, A. K. Kryukov +2
This article studies the rotational dynamics of three identical coupled pendulums. There exist two parameter areas where the in-phase rotational motion is unstable and out-of-phase…
The dynamics of ensemble of neuron-like elements with excitatory couplings
Alexander G. Korotkov, Alexey O. Kazakov, Tatiana A. Levanova +1
We study the phenomenological model of ensemble of two FitzHugh-Nagumo neuron-like elements with symmetric excitatory couplings. The main advantage of proposed model is the new app…
The impact of electrical couplings on the sequential bursting activity in the ensemble of inhibitory coupled Van der Pol elements
T. A. Levanova, A. O. Kazakov, A. G. Korotkov +1
The new phenomenological model of the ensemble of three neurons with chemical (synaptic) and electrical couplings has been studied. One neuron is modeled by a single Van der Pol os…
Heteroclinic and homoclinic structures in the system of four identical globally coupled phase oscillators with nonpairwise interactions of phases
Evgeny A. Grines, Grigory V. Osipov
Systems of identical globally coupled phase oscillators can demonstrate a multitude of complex behaviours. Such systems can have chaotic dynamics for when a coupling func…
Spiral attractors as the root of a new type of "bursting activity" in the Rosenzweig-MacArthur model
Yu. V. Bakhanova, A. O. Kazakov, A. G. Korotkov +2
We study the peculiarities of spiral attractors in the Rosenzweig-MacArthur model, that describes dynamics in a food chain "prey-predator-superpredator". It is well-known that spir…
Chimera patterns in the Kuramoto-Battogtokh model
L. A. Smirnov, G. V. Osipov, A. Pikovsky
Kuramoto and Battogtokh [Nonlinear Phenom. Complex Syst. 5, 380 (2002)] discovered chimera states represented by stable coexisting synchrony and asynchrony domains in a lattice of…
Mixed mode synchronization and network bursting of neurons with post-inhibitory rebound
Roman Nagornov, Grigory Osipov, Maxim Komarov +2
This study is focused on the mechanisms of rhythmogenesis and robustness of anti-phase bursting in half-center-oscillators (HCOs) consisting of two reciprocally inhibitory coupled…
Coherence properties of cycling chaos
T. A. Levanova, G. V. Osipov, A. Pikovsky
Cycling chaos is a heteroclinic connection between several chaotic attractors, at which switching between the chaotic sets occur at growing time intervals. Here we characterize the…
Synchronized bursts following instability of synchronous spiking in chaotic neuronal networks
Mikhail V. Ivanchenko, Grigory V. Osipov, Vladimir D. Shalfeev +1
We report on the origin of synchronized bursting dynamics in various networks of neural spiking oscillators, when a certain threshold in coupling strength is exceeded. These ensemb…