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Patrick Louodop

Publications and source records attributed to Patrick Louodop.

16 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↗
arXiv2026

Characterizing some dynamical states in swarmalators system using recurrence analysis

Chimera or chimera-like states arise in a wide variety of networks and their identification remains challenging particularly when mobility prevents index-based ordering of the nodes. In this work, we propose a recurrence analysis based method to identify and characterize chimera states in two distinct dynamical frameworks: a network of chaotic Colpitts oscillators and a system of swarmalators where delayed interactions induce chimera-like dynamics named boiling state. The suggested strategy is based on the joint recurrence plots and entropy-based measures, to capture the spatio-temporal organization. This approach enables a clear discrimination between complete synchronization, quasi-synchronization and disordered regimes, even when conventional order parameters yield ambiguous results. Furthermore, we introduce the degree of independence, which estimates the proportion of dynamically completely independent nodes in the system. This measure provides a robust characterization of transitions between collective states.

nlin.AO↗
arXiv2025

Traveling chimeras and collective coordination in beta-cell networks

Pancreatic $\beta$-cells play a central role in maintaining glucose homeostasis through the pulsatile secretion of insulin. This essential function relies not only on intracellular regulatory mechanisms but also on coordinated interactions among $\beta$-cells within the islets of Langerhans. Disruptions in this intercellular coordination are increasingly implicated in metabolic disorders such as type~I and type~II diabetes. In this work, we employ a computational framework to investigate the collective dynamics of a network of coupled $\beta$-cells interacting through a nonlocally coupled ring topology that incorporates both electrical and metabolic coupling pathways. This topology captures short- and long-range interactions known to shape islet communication. Numerical simulations reveal a variety of emergent behaviors, including synchronization, traveling waves, and traveling chimera states, in which coherent and incoherent domains coexist and propagate across the network. These findings provide new insight into the mechanisms governing coordinated $\beta$-cell activity and the regulation of pulsatile insulin secretion. By clarifying how coupling structure and intercellular communication shape islet-wide dynamics, this work contributes to a deeper understanding of the dysfunctions underlying diabetes.

physics.bio-ph↗
arXiv2025

Topological transitions in swarmalators systems

After its development, the swarmalators model attracted a great deal of attention since it was found to be very suitable to reproduce several behaviors in collective dynamics. However, few works explain the transitions that are observed while varying system parameters. In this letter, we demonstrate that the changes observed in swarmalator dynamics are governed by changes in the system's topology. To provide a deeper understanding of these changes, we present a topological framework for the swarmalator system and determine the topological charge $Q$ and the helicity $\gamma$ of the corresponding topology. Investigations on synchronization and transition to synchronization are studied using this topological charge and the variance of the helicity.

nlin.AO↗
arXiv2025

Energy-dynamics interplay in temporal networks triggers explosive synchronization

Synchronization in networks of coupled oscillators is a fundamental problem in the study of collective behavior. In this paper, we investigate the synchronization transition in networks of coupled dynamical systems from an energetic perspective. Interactions between systems/oscillators are assumed to be governed by one of the following mechanisms: (i) the intrinsic energy $\mathbf{H}$, describing the conservative internal dynamics of isolated systems, and (ii) the dissipative energy $\dot{\mathbf{H}}$, accounting for energy losses and exchanges due to interactions and damping. An energetic threshold is introduced to modulate the network connectivity, so that the topology evolves in time according to the instantaneous energetic similarity between systems, allowing us to analyze how the balance between intrinsic and dissipative energy shapes the transition to synchronization. Using the R\"ossler and Lorenz systems as representative examples, while keeping the framework general and applicable to other dynamical systems, we explore three representative dynamical regimes: periodic, multiperiodic, and chaotic. This reveals that, the nature of the synchronization transition strongly depends on the interplay between microscopic dynamics and the mesoscopic connectivity structure. In particular, chaotic oscillators coupled through intrinsic energy favor explosive synchronization, corresponding to a first-order transition, whereas periodic and multiperiodic dynamics lead to smooth second-order transitions. In contrast, dissipative-energy-based connectivity suppresses first-order transitions in chaotic networks but can induce second-order transition in multiperiodic systems.

nlin.AO↗
arXiv2025

Mobile oscillators in a mobile multi-cluster network

Different collective behaviors emerging from the unknown have been examined in networks of mobile agents in recent years. Mobile systems, far from being limited to modeling and studying various natural and artificial systems in motion and interaction, offer versatile solutions across various domains, facilitating tasks ranging from navigation and communication to data collection and environmental monitoring. We examine the relative mobility between clusters, each composed of different elements in a multi-clusters network-a system composed of clusters interconnected to form a larger network of mobile oscillators. Each mobile oscillator exhibits both external (i.e., position in a 2D space) and internal dynamics (i.e., phase oscillations). Studying the mutual influence between external and internal dynamics, often leads the system towards a state of synchronization within and between clusters. We show that synchronization between clusters is affected by their spatial closeness. The stability of complete synchronization observed within the clusters is demonstrated through analytical and numerical methods.

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↗
arXiv2024

Chimera state in neural network with the Proportional-Integral-Derivative coupling

This study delves into the emergence of collective behaviors within a network comprising interacting cells. Each cell integrates a fixed number of neurons governed by an activation gradient based on Hopfield's model. The intra-cell interactions among neurons are local and directed, while inter-cell connections are facilitated through a PID (Proportional-Integral-Derivative) coupling mechanism. This coupling introduces an adaptable environmental variable, influencing the network dynamics significantly. Numerical simulations employing three neurons per cell across a network of fifty cells reveal diverse dynamics, including incoherence, coherence, synchronization, chimera states, and traveling wave. These phenomena are quantitatively assessed using statistical measures such as the order parameter, strength of incoherence, and discontinuity measure. Variations of the resistive, inductive, or capacitive couplings of the inter-cell environment are explored and their effects are analysed. Furthermore, the study identifies multistability in network dynamics, characterized by the coexistence of multiple stable states for the same set of parameters but with different initial conditions. A linear augmentation strategy is employed for its control.

nlin.PS↗
arXiv2022

Synchronization in a multilevel network using the Hamilton-Jacobi-Bellman (HJB) technique

This paper presents the optimal control and synchronization problem of a multilevel network of Rössler chaotic oscillators. Using the Hamilton-Jacobi-Bellman (HJB) technique, the optimal control law with three-state variables feedback is designed such that the trajectories of all the Rössler oscillators in the network are optimally synchronized in each level. Furthermore, we provide numerical simulations to demonstrate the effectiveness of the proposed approach for the cases of one and three networks. A perfect correlation between the MATLAB and the PSPICE results was obtained, thus allowing the experimental validation of our designed controller and shows the effectiveness of the theoretical results.

math.OC↗
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↗
arXiv2020

Dynamics of multilayer networks with amplification

We study the dynamics of a multilayer network of chaotic oscillators subject to an amplification. Previous studies have proven that multilayer networks present phenomena such as synchronization, cluster and chimera states. Here we consider a network with two layers of Roessler chaotic oscillators as well as applications to multilayer networks of chaotic jerk and Lienard oscillators. Intralayer coupling is considered to be all to all in the case of Roessler oscillators, a ring for jerk oscillators and global mean field coupling in the case of Lienard, the interlayer coupling is unidirectional in all these three cases. The second layer has an amplification coefficient. An in depth study on the case of a network of Roessler oscillators using master stability function and order parameter leads to several phenomena such as complete synchronization, generalized, cluster and phase synchronization with amplification. For the case of Roessler oscillators, we note that there are also certain values of coupling parameters and amplification where the synchronization does not exist or the synchronization can exist but without amplification. Using other systems with different topologies, we obtain some interesting results such as chimera state with amplification, cluster state with amplification and complete synchronization with amplification.

nlin.AO↗
arXiv2016

Coherent libration to coherent rotational dynamics via chimeralike states and clustering in Josephson Junction array

An array of excitable Josephson junctions under global mean-field interaction and a common periodic forcing shows emergence of two important classes of coherent dynamics, librational and rotational motion in the weaker and stronger coupling limits, respectively, with transitions to chimeralike states and clustered states in the intermediate coupling range. In this numerical study, we use the Kuramoto complex order parameter and introduce two measures, a libration index and a clustering index to characterize the dynamical regimes and their transition and locate them in a parameter plane.

nlin.CD↗
arXiv2013

Finite-time synchronization of tunnel diode based chaotic oscillators

This paper addresses the problem of finite-time synchronization of tunnel diode based chaotic oscillators. After a brief investigation of its chaotic dynamics, we propose an active adaptive feedback coupling which accomplishes the synchronization of tunnel diode based chaotic systems with and without the presence of delay(s), basing ourselves on Lyapunov and on Krasovskii-Lyapunov stability theories. This feedback coupling could be applied to many other chaotic systems. A finite horizon can be arbitrarily established by ensuring that chaos synchronization is achieved at a pre-established time. An advantage of the proposed feedback coupling is that it is simple and easy to implement. Both mathematical investigations and numerical simulatio

nlin.CD↗