Spatial coexistence of coherent and incoherent dynamics in network coupled oscillators is called a chimera state. We study such states neurons without any direct interactions but connected through another medium neurons, forming multilayer structure. The upper layer thus made up uncoupled the lower plays role which share information among each other. Hindmarsh-Rose with square wave bursting are considered as nodes both layers. In addition, we also discuss existence presence inter...

We study the existence of chimera states in pulse-coupled networks bursting Hindmarsh-Rose neurons with nonlocal, global, and local (nearest neighbor) couplings. Through a linear stability analysis, we discuss behavior function incoherent (i.e., disorder), coherent, chimera, multichimera states. Surprisingly, find that occur even using nearest neighbor interaction network identical alone. This is contrast populations nonlocally or globally coupled oscillators. A chemical synaptic coupling...

We study the emergence of chimera states in a multilayer neuronal network, where one layer is composed coupled and other uncoupled neurons. Through structure, with neurons acts as medium by means which share information spite absent physical connections among them. Neurons are connected electrical synapses, while across two layers through chemical synapses. In both dynamics each neuron described Hindmarsh-Rose square wave bursting dynamics. show that presence different types connecting...

We study excitation and suppression of chimera states in an ensemble nonlocally coupled oscillators arranged a framework multiplex network. consider the homogeneous network (all identical oscillators) with different parametric cases interlayer heterogeneity by introducing parameter mismatch between layers. show feasibility to suppress via moderate interaction layer exhibiting state other layers which are coherent or incoherent state. On contrary, for larger coupling, we observe emergence...

In this paper, we report the occurrence of chimera patterns in a network neuronal oscillators, which are coupled through local, synaptic gradient coupling. We discover new pattern, namely imperfect traveling state, where incoherent domain spreads into coherent network. Remarkably, also find that states arise even for one-way local coupling, is contrast to earlier belief only nonlocal, global, or nearest-neighbor coupling can give rise state; further relaxes essential connectivity requirement...

Collective behavior among coupled dynamical units can emerge in various forms as a result of different coupling topologies well types functions. Chimera states have recently received ample attention fascinating manifestation collective behavior, particular describing symmetry breaking spatiotemporal pattern where synchronized and desynchronized coexist network oscillators. In this perspective, we review the emergence chimera states, focusing on effects that describe interaction connecting We...

Abstract Interactions amongst agents frequently exist only at particular moments in time, depending on their closeness space and movement parameters. Here we propose a minimal model of moving where the network contacts changes over time due to motion. In particular, interact based proximity two-dimensional space, but if they belong same fixed interaction zones. Our research reveals emergence global synchronization all zones are attractive. However, some repulsive, deflect synchrony lead...

The tumor-immune interactive dynamics is an evergreen subject that continues to draw attention from applied mathematicians and oncologists, especially so due the unpredictable growth of tumor cells. In this respect, mathematical modeling promises insights might help us better understand harmful aspect our biology. With goal, we here present study a model describes how cells evolve survive brief encounter with immune system, mediated by effector host We focus on distribution eigenvalues...

Abstract Swarmalators are entities with the simultaneous presence of swarming and synchronization that reveal emergent collective behavior due to fascinating bidirectional interplay between phase spatial dynamics. Although different coupling topologies have already been considered, here we introduce time-varying competitive interaction among swarmalators where underlying connectivity for attractive repulsive varies depending on vision (sensing) radius. Apart from investigating some...

Recent developments in complex systems have witnessed that many real-world scenarios, successfully represented as networks, are not always restricted to binary interactions but often include higher-order among the nodes. These beyond pairwise preferably modeled by hypergraphs, where hyperedges represent between a set of In this work, we consider multiplex network intralayer connections called hypergraph. The hypergraph is constructed mapping maximal cliques scale-free suitable sizes. We...

Since the discovery of chimera states, presence a nonzero phase lag parameter turns out to be an essential attribute for emergence chimeras in nonlocally coupled identical Kuramoto oscillators' network with pairwise interactions. In this Letter, we report without owing introduction nonpairwise The influence added nonlinearity system dynamics form simplicial complexes mitigates requisite states. Chimera states stimulated by reciprocity and interaction strengths their multistable nature are...

Understanding how the interplay between higher-order and multilayer structures of interconnections influences synchronization behaviors dynamical systems is a feasible problem interest, with possible application in essential topics such as neuronal dynamics. Here, we provide comprehensive approach for analyzing stability complete state simplicial complexes numerous interaction layers. We show that exists an invariant solution derive necessary condition stable presence general coupling...

We study a population of swarmalators (swarming/mobile oscillators) which run on ring and are subject to random pinning. The pinning represents the tendency particles stick defects in underlying medium competes with sync / swarm. result is rich collective behavior. A highlight low dimensional chaos systems ordinary, Kuramoto-type oscillators uncommon. Some states (the phase wave split wave) resemble those seen Janus matchsticks or Japanese tree frogs. others (such as unsteady states) may be...

Abstract Synchronization has received a lot of attention from the scientific community for systems evolving on static networks or higher-order structures, such as hypergraphs and simplicial complexes. In many relevant real-world applications, latter are not but do evolve in time, this work we thus discuss impact time-varying nature structures emergence global synchronization. To achieve goal, extend master stability formalism to account, general way, additional contributions arising time...

Self-organized bistability (SOB) stands as a critical behavior for the systems delicately adjusting themselves to brink of bistability, characterized by first-order transition. Its essence lies in inherent ability system undergo enduring shifts between coexisting states, achieved through self-regulation controlling parameter. Recently, SOB has been established scale-free network recurrent transition short-living state global synchronization. Here, we embark on theoretical exploration that...

Much research has in recent years been devoted to better our understanding of the intricate relationships between ecology and evolutionary success species. These explorations have often focused on complex interplay among ecological factors rhythms species various environments. Central these studies is concept survival fittest, proposed by Charles Darwin, where circumstances, portrayed as social dilemmas, favour welfare self-interested over others. To further advance this line research, we...

Networks incorporating higher-order interactions are increasingly recognized for their ability to introduce novel dynamics into various processes, including synchronization. Previous studies on synchronization within multilayer networks have often been limited specific models, such as the Kuramoto model, or focused solely individual layers. Here, we present a comprehensive framework investigating synchronization, particularly global in with interactions. Our considers beyond pairwise...