arXiv subjects

Robert Tchitnga

Publications and source records attributed to Robert Tchitnga.

5 recordsLinked to original sources

arXiv2026

Chimera state in a neuronal network under the action of a magnetic field

The Hindmarsh-Rose (HR) neuronal network has recently been the subject of studies highlighting the influence of the electric field on the chimera states within it. In this study, we demonstrate the influence of the magnetic field on three categories of chimera states previously discovered in the same network: the traveling chimera state, the traveling multicluster chimera state, and the traveling multicluster chimera breather. The study is entirely numerical and proceeds in each case with three different applications of the magnetic field: first, the entire network is subjected to the field; then, half of the network is subjected to it; and finally, two symmetrical but distinct regions are also subjected to the field. Several phenomena emerge, the most notable of which are the multitraveling chimera state and the multialternating chimera state. This thus illustrates the ability of the magnetic field to transform areas of incoherence into areas of coherence, thus enriching the synchronization field and throwing more light on the field's influence on brain cells.

nlin.AO↗

arXiv2025

Attractive-repulsive challenge in swarmalators with time-dependent speed

We examine a network of entities whose internal and external dynamics are intricately coupled, modeled through the concept of ``swarmalators'' as introduced by O'Keeffe et al. \textcolor{blue}{\cite{o2017oscillators}}. We investigate how the entities' natural velocities impact the network's collective dynamics and path to synchronization. Specifically, we analyze two scenarios: one in which each entity has an individual natural velocity, and another where a group velocity is defined by the average of all velocities. Our findings reveal two distinct forms of phase synchronization -- static and rotational -- each preceded by a complex state of attractive-repulsive interactions between entities. This interaction phase, which depends sensitively on initial conditions, allows for selective modulation within the network. By adjusting initial parameters, we can isolate specific entities to experience attractive-repulsive interactions distinct from the group, prior to the onset of full synchronization. This nuanced dependency on initial conditions offers valuable insights into the role of natural velocities in tuning synchronization behavior within coupled dynamic networks.

nlin.AO↗

arXiv2024

Expected and unexpected routes to synchronization in a system of swarmalators

Systems of oscillators whose internal phases and spatial dynamics are coupled, swarmalators, present diverse collective behaviors which in some cases lead to explosive synchronization in a finite population as a function of the coupling parameter between internal phases. Near the synchronization transition, the phase energy of the particles is represented by the XY model, and they undergo a transition which can be of the first order or second depending on the distribution of natural frequencies of their internal dynamics. The first order transition is obtained after an intermediate state (Static Wings Phase Wave state (SWPW)) from which the nodes, in cascade over time, achieve complete phase synchronization at a precise value of the coupling constant. For a particular case of natural frequencies distribution, a new phenomenon of Rotational Splintered Phase Wave state (RSpPW) is observed and leads progressively to synchronization through clusters switching alternatively from one to two and for which the frequency decreases as the phase coupling increases.

nlin.AO↗

arXiv2021

Traveling chimera patterns in two-dimensional neuronal network

We study the emergence of the traveling chimera state in a two-dimensional network of Hindmarsh-Rose burst neurons with the mutual presence of local and non-local couplings. We show that in the unique presence of the non-local chemical coupling modeled by a nonlinear function, the traveling chimera phenomenon occurs with a displacement in both directions of the plane of the grid. The introduction of local electrical coupling shows that the mutual influence of the two types of coupling can, for certain values, generate traveling chimera, imperfect-traveling, traveling multi-clusters, and alternating traveling chimera, ie the presence in the network under study, of patterns of coherent elements interspersed by other incoherent elements in movement and alternately changing their position over time. The confirmation of the states of coherence is done by introducing the parameter of instantaneous local order parameter in two dimensions. We extend our analysis through mathematical tools such as the Hamilton energy function to determine the direction of propagation of patterns in two dimensions.

nlin.PS↗

arXiv2021

Chimera states in a neuronal network under the action of an electric field

The phenomenon of the chimera state symbolizes the coexistence of coherent and incoherent sections of a given population. This phenomenon identified in several physical and biological systems presents several variants, including the multichimera states and the traveling chimera state. Here, we numerically study the influence of a weak external electric field on the dynamics of a network of Hindmarsh-Rose (HR) neurons coupled locally by an electrical interaction and nonlocally by a chemical one. We first focus on the phenomena of traveling chimera states and multicluster oscillating breathers that appear in the electric field's absence. Then in the field's presence, we highlight the presence of a chimera state, a multichimera state, an alternating chimera state and a multicluster traveling chimera.

nlin.AO↗