arXiv subjects

A. V. Bukh

Publications and source records attributed to A. V. Bukh.

6 recordsLinked to original sources

arXiv2026

Extreme forcing and wave dynamics in weakly nonlocally coupled excitable FitzHugh-Nagumo systems

The influence of extreme external forcing on traveling-wave dynamics in an ensemble of weakly nonlocally coupled excitable FitzHugh--Nagumo systems is studied. Three types of external exposure are considered: periodic Gaussian pulses, periodic pulses modulated by Gaussian white noise, and Lévy noise with tunable distribution parameters. Periodic forcing produces synchronization tongues with highly regular collective dynamics and may induce multiple traveling waves or coexistence of partial synchronization with wave propagation. In contrast, Lévy noise suppresses regular behavior and generates a regime of counter-propagating waves, which with increasing intensity transitions to random walking dynamics. The study provides a comprehensive classification of the observed dynamical regimes and presents their organization in parameter space for different types of extreme external forcing.

nlin.AO↗

arXiv2025

Effect of Levy noise on the network of coupled Chialvo neurons: Impact of topology

This research investigates the complex spatiotemporal behaviors of Chialvo neuron maps under the influence of Levy noise on three different network topologies that is a ring network, a two dimensional lattice affected by electromagnetic flux, and a delayed coupled lattice. On the ring structure, we show that adding non uniform Levy noise induces the formation of new collective dynamics like standing and traveling waves. The frequency and type of these emergent patterns depend sensitively on the intrinsic excitability parameter and the noise intensity, revealing new pathways to control synchronization behavior through noise modulation. In the 2D lattice network, we show that electromagnetic flux and noise together induce a diverse range of behaviors, from synchronized waves to desynchronized states. Most strikingly, spiral wave chimeras emerge under moderate noise, with coherent and incoherent regions coexisting, highlighting the fine balance between external forcing and stochastic perturbations. Finally, upon introducing delay in the lattice structure, the system displays a rich variety of dynamical regimes such as labyrinth patterns, rotating spirals, and target waves whose stability and transitions are greatly affected by both delay and coupling strength.

nlin.AO↗

arXiv2023

Role of coupling delay in oscillatory activity in autonomous networks of excitable neurons with dissipation

We study numerically the effects of time delay in networks of delay-coupled excitable FitzHugh Nagumo systems with dissipation. The generation of periodic self-sustained oscillations and its threshold are analyzed depending on the dissipation of a single neuron, the delay time, and random initial conditions. The peculiarities of spatiotemporal dynamics of time-delayed bidirectional ring-structured FitzHugh-Nagumo neuronal systems are investigated in cases of local and nonlocal coupling topology between the nodes, and a first-order nonequilibrium phase transition to synchrony is established. It is shown that the emergence of oscillatory activity in delay-coupled FitzHugh-Nagumo neurons is observed for smaller values of the coupling strength as the dissipation parameter decreases. This can provide the possibility of controlling the spatiotemporal behavior of the considered neuronal networks. The observed effects are quantified by plotting distributions of the maximal Lyapunov exponent and the global order parameter in terms of delay and coupling strength.

nlin.AO↗

arXiv2020

Quantifying the transition from spiral waves to spiral wave chimeras in a lattice of self-sustained oscillators

The present work is devoted to the detailed quantification of the transition from spiral waves to spiral wave chimeras in a network of self-sustained oscillators with two-dimensional geometry. The basic elements of the networks are the van der Pol oscillator and the FitzHugh-Nagumo neuron. Both models are in the regime of relaxation oscillations. We analyze the regime by using the indices of local sensitivity which enables us to evaluate the sensitivity of each individual oscillator at finite time. Spi-ral waves are observed in both lattices when the interaction between elements have the local character. The dynamics of all the elements is regular. There are no high-sensitive regions. We have discovered that when the coupling becomes nonlocal, the features of the systems significantly changes. The oscillation regime of the spiral wave center element switches to chaotic one. Besides this, a region with high sensitivity occurs around this oscillator. Moreover, we show that the latter expands in space with elongation of the coupling range. As a result, an incoherence cluster of the spiral wave chimera is formed exactly within this high-sensitive area. Formation of this cluster is accompanied by the sharp increase in values of the maximal Lyapunov exponent to the positive region. Furthermore, we explore that the system can even switch to hyperchaotic regime, when several Lyapunov exponents becomes positive.

nlin.AO↗

arXiv2020

Role of solitary states in forming spatiotemporal patterns in a 2D lattice of van der Pol oscillators

The behavior of the ensemble of coupled van der Pol oscillators is abundant when coupling parameters are changed. Incoherent and chimera-like regimes are observed at small values of the coupling strength parameter. Synchronization takes place with an increase in the coupling strength and coupling range parameters. Various chimera and solitary states are realised when the coupling strength parameter is sufficiently large. The single van der Pol oscillator is taken in the regime of relaxation oscillations. Therefore, the lattice may realise spiral wave and spiral wave chimera regimes. Besides, target wave and solitary state regimes are observed in the ensemble. Finally, the solitary state and solitary state chimera regimes are firstly shown for the lattice of coupled van der Pol oscillators.

nlin.AO↗

arXiv2017

Local sensitivity of spatiotemporal structures

We present an index for the local sensitivity of spatiotemporal structures in coupled oscillatory systems based on the asymptotic scaling of local-in-space, finite-time Lyapunov Exponents. For a system of nonlocally-coupled Rössler oscillators, we show that deviations of this index reflect the sensitivity to noise and the onset of spatial chaos for the patterns where coherence and incoherence regions coexist.

math.DS↗