arXiv subjects

Volodymyr Maistrenko

Publications and source records attributed to Volodymyr Maistrenko.

4 recordsLinked to original sources

arXiv2025

Parallelization of Network Dynamics Computations in Heterogeneous Distributed Environment

This paper addresses the problem of parallelizing computations to study non-linear dynamics in large networks of non-locally coupled oscillators using heterogeneous computing resources. The proposed approach can be applied to a variety of non-linear dynamics models with runtime specification of parameters and network topologies. Parallelizing the solution of equations for different network elements is performed transparently and, in contrast to available tools, does not require parallel programming from end-users. The runtime scheduler takes into account the performance of computing and communication resources to reduce downtime and to achieve a quasi-optimal parallelizing speed-up. The proposed approach was implemented, and its efficiency is proven by numerous applications for simulating large dynamical networks with 10^3-10^8 elements described by Hodgkin-Huxley, FitzHugh-Nagumo, and Kuramoto models, for investigating pathological synchronization during Parkinson's disease, analyzing multi-stability, for studying chimera and solitary states in 3D networks, etc. All the above computations may be performed using symmetrical multiprocessors, graphic processing units, and a network of workstations within the same run and it was demonstrated that near-linear speed-up can be achieved for large networks. The proposed approach is promising for extension to new hardware like edge-computing devices.

nlin.CD↗

arXiv2021

Scroll ring chimera states in oscillatory networks

We report the appearance of a scroll ring and scroll toroid chimera states from the proposed initial conditions for the Kuramoto model of coupled phase oscillators in the 3D grid topology with inertia. The proposed initial conditions provide an opportunity to obtain as single as well as multiple scroll ring and toroid chimeras with different major and minor diameters. We analyze their properties and demonstrate, in particular, the patterns of coherent, partially coherent, and incoherent scroll ring chimera states with different structures of filaments and chaotic oscillators. Those patterns can coexist with solitary states and solitary patterns in the oscillatory networks.

nlin.PS↗

arXiv2020

Spiral wave chimeras for coupled oscillators with inertia

We report the appearance and the metamorphoses of spiral wave chimera states in coupled phase oscillators with inertia. First, when the coupling strength is small enough, the system behavior resembles classical two-dimensional (2D) Kuramoto-Shima spiral chimeras with bell-shape frequency characteristic of the incoherent cores. As the coupling increases, the cores acquire concentric regions of constant time-averaged frequencies, the chimera becomes quasiperiodic. Eventually, with a subsequent increase in the coupling strength, only one such region is left, i.e., the whole core becomes frequency-coherent. An essential modification of the system behavior occurs, when the parameter point enters the so-called solitary} region. Then, isolated oscillators are normally present on the spiral core background of the chimera states. These solitary oscillators do not participate in the common spiraling around the cores; instead, they start to oscillate with different time-averaged frequencies (Poincaré winding numbers). The number and the disposition of solitary oscillators can be any, given by the initial conditions. At a further increase in the coupling, the spiraling disappears, and the system behavior passes to a sort of spatiotemporal chaos.

nlin.AO↗

arXiv2017

Multiple scroll wave chimera states

We refer the appearance of three-dimensional (3D) multiheaded chimera states that display cascades of self-organized spatiotemporal patterns of coexisting coherence and incoherence. We demonstrate that number of the incoherent chimera's domains can grow additively under appropriate varying the system parameters generating thereby head-adding cascades of the scroll wave chimeras. The phenomenon is derived for Kuramoto model of N identical phase oscillators placed in the 3D cube with periodic boundary conditions, parameters are coupling radius $r$ and phase lag $α$. To obtain the multiheaded chimeras, we perform the so-called 'cloning procedure' as follows: choose a sample single-headed 3D chimera state, make appropriate scale transformation, and put some number of copies of them into the unit cube. After, start numerical simulations with slightly perturbed initial conditions for long enough time to confirms or denies the state existence and stability. It is found, by this a way, that multiple scroll wave chimeras including those with incoherent rolls, Hopf links and trefoils admit this sort of multiheaded regeneration. On the other hand, multiple 3D chimeras without spiral rotations, like coherent and incoherent balls, tubes, crosses, and layers appear to be unstable under are destroyed rather fast even with any small perturbations.

nlin.PS↗