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In a chain of mutually coupled oscillators, the coupling threshold for synchronization between the outermost identical oscillators decreases when a type of impurity (in terms of parameter mismatch) is introduced in the inner oscillator(s). The outer oscillators interact indirectly via dynamic relaying, mediated by the inner oscillator(s). We confirm this enhancing of critical coupling in the chaotic regimes of the Lorenz system, in the Rössler system in the absence of coupling delay, and in the Mackey-Glass system with delay coupling. The enhancing effect is experimentally verified in the electronic circuit of Rössler oscillators. [ABSTRACT FROM AUTHOR]

Different aspects of synchronization emerging in networks of coupled oscillators have been examined prominently in the last decades. Nevertheless, little attention has been paid on the emergence of this imperative collective phenomenon in networks displaying temporal changes in the connectivity patterns. However, there are numerous practical examples where interactions are present only at certain points of time owing to physical proximity. In this work, we concentrate on exploring the emergence of interlayer and intralayer synchronization states in a multiplex dynamical network comprising of layers having mobile nodes performing two-dimensional lattice random walk. We thoroughly illustrate the impacts of the network parameters, in particular, the vision range ϕ and the step size u together with the inter- and intralayer coupling strengths ε and k on these synchronous states arising in coupled Rössler systems. The presented numerical results are very well validated by analytically derived necessary conditions for the emergence and stability of the synchronous states. Furthermore, the robustness of the states of synchrony is studied under both structural and dynamical perturbations. We find interesting results on interlayer synchronization for a continuous removal of the interlayer links as well as for progressively created static nodes. We demonstrate that the mobility parameters responsible for intralayer movement of the nodes can retrieve interlayer synchrony under such structural perturbations. For further analysis of survivability of interlayer synchrony against dynamical perturbations, we proceed through the investigation of single-node basin stability, where again the intralayer mobility properties have noticeable impacts. We also discuss the scenarios related mainly to effects of the mobility parameters in cases of varying lattice size and percolation of the whole network. [ABSTRACT FROM AUTHOR]

In this paper, we report the occurrence of chimera patterns in a network of neuronal oscillators, which are coupled through local, synaptic gradient coupling. We discover a new chimera pattern, namely the imperfect traveling chimera state, where the incoherent traveling domain spreads into the coherent domain of the network. Remarkably, we also find that chimera states arise even for one-way local coupling, which is in contrast to the earlier belief that only nonlocal, global, or nearest-neighbor local coupling can give rise to chimera state; this find further relaxes the essential connectivity requirement of getting a chimera state. We choose a network of identical bursting Hindmarsh-Rose neuronal oscillators, and we show that depending upon the relative strength of the synaptic and gradient coupling, several chimera patterns emerge. We map all the spatiotemporal behaviors in parameter space and identify the transitions among several chimera patterns, an in-phase synchronized state, and a global amplitude death state. [ABSTRACT FROM AUTHOR]

We study the existence of chimera states in a network of locally coupled chaotic and limit-cycle oscillators. The necessary condition for chimera state in purely local coupled oscillators is discussed. At first, we numerically observe the existence of chimera or multichimera states in the locally coupled Hindmarsh-Rose neuron model. We find that delay time in the nonlinear local coupling reduces the domain of the coherent island in the parameter space of the synaptic coupling strength and time delay, and thus the coherent region can be completely eliminated once the time delay exceeds a certain threshold. We then consider another form of nonlinearity in the local coupling, and the existence of chimera states is observed in the time-delayed Mackey-Glass system and in a Van der Pol oscillator. We also discuss the effect of time delay in local coupling for the existence of chimera states in Mackey-Glass systems. The nonlinearity present in the coupling function plays a key role in the emergence of chimera or multichimera states. A phase diagram for the chimera state is identified over a wide parameter space. [ABSTRACT FROM AUTHOR]

We study the existence of chimera states in pulse-coupled networks of bursting Hindmarsh-Rose neurons with nonlocal, global, and local (nearest neighbor) couplings. Through a linear stability analysis, we discuss the behavior of the stability function in the incoherent (i.e., disorder), coherent, chimera, and multichimera states. Surprisingly, we find that chimera and multichimera states occur even using local nearest neighbor interaction in a network of identical bursting neurons alone. This is in contrast with the existence of chimera states in populations of nonlocally or globally coupled oscillators. A chemical synaptic coupling function is used which plays a key role in the emergence of chimera states in bursting neurons. The existence of chimera, multichimera, coherent, and disordered states is confirmed by means of the recently introduced statistical measures and mean phase velocity. [ABSTRACT FROM AUTHOR]

We report intermittent large spiking events in a heterogeneous network of forced Josephson junctions under the influence of repulsive interaction. The response of the individual junctions has been inspected instead of the collective response of the ensemble, which reveals the large spiking events in a subpopulation with characteristic features of extreme events (EE). The network splits into three clusters of junctions, one in coherent libration, one in incoherent rotational motion, and another subpopulation originating EE, which resembles a chimeralike pattern. EE migrates spatially from one to another subpopulation of junctions with the repulsive strength. The origin of EE in a subpopulation and chimera pattern is a generic effect of distributed damping parameter and repulsive interaction, which we verify with another network of the Liénard system. EE originates in the subpopulation via a local riddling of in-phase synchronization. The probability density function of event heights confirms the rare occurrence of large events and the return time of EE as expressed by interevent intervals in the subgroup follows a Poisson distribution. The mechanism of the origin of such a unique clustering is explained qualitatively. [ABSTRACT FROM AUTHOR]

We investigate interlayer synchronization in a stochastic multiplex hypernetwork which is defined by the two types of connections, one is the intralayer connection in each layer with hypernetwork structure and the other is the interlayer connection between the layers. Here all types of interactions within and between the layers are allowed to vary with a certain rewiring probability. We address the question about the invariance and stability of the interlayer synchronization state in this stochastic multiplex hypernetwork. For the invariance of interlayer synchronization manifold, the adjacency matrices corresponding to each tier in each layer should be equal and the interlayer connection should be either bidirectional or the interlayer coupling function should vanish after achieving the interlayer synchronization state. We analytically derive a necessary-sufficient condition for local stability of the interlayer synchronization state using master stability function approach and a sufficient condition for global stability by constructing a suitable Lyapunov function. Moreover, we analytically derive that intralayer synchronization is unattainable for this network architecture due to stochastic interlayer connections. Remarkably, our derived invariance and stability conditions (both local and global) are valid for any rewiring probabilities, whereas most of the previous stability conditions are only based on a fast switching approximation. [ABSTRACT FROM AUTHOR]

The coexistence of coherent and incoherent domains, namely the appearance of chimera states, has been studied extensively in many contexts of science and technology since the past decade, though the previous studies are mostly built on the framework of one-dimensional and two-dimensional interaction topologies. Recently, the emergence of such fascinating phenomena has been studied in a three-dimensional (3D) grid formation while considering only the nonlocal interaction. Here we study the emergence and existence of chimera patterns in a three-dimensional network of coupled Stuart-Landau limit-cycle oscillators and Hindmarsh-Rose neuronal oscillators with local (nearest-neighbor) interaction topology. The emergence of different types of spatiotemporal chimera patterns is investigated by taking two distinct nonlinear interaction functions. We provide appropriate analytical explanations in the 3D grid of the network formation and the corresponding numerical justifications are given. We extend our analysis on the basis of the Ott-Antonsen reduction approach in the case of Stuart-Landau oscillators containing infinite numbers of oscillators. Particularly, in the Hindmarsh-Rose neuronal network the existence of nonstationary chimera states is characterized by an instantaneous strength of incoherence and an instantaneous local order parameter. Besides, the condition for achieving exact neuronal synchrony is obtained analytically through a linear stability analysis. The different types of collective dynamics together with chimera states are mapped over a wide range of various parameter spaces. [ABSTRACT FROM AUTHOR]

Synchronization in time-varying complex dynamical systems has been explored in a variety of different coupling topologies during the last two decades. In most of the previous cases, the basic time-varying coupling topologies were considered to be a single interaction between the nodes or in a monolayer configuration, although in many real situations the types of interactions are more than one or in the form of multilayer. In this work, we study the synchronization in multiplex neuronal network, which evolves with time, and each layer consists of more than one interaction function. Specifically, we consider a neuronal hypernetwork at each layer in which neurons are communicated with each other via electrical and chemical synapses simultaneously and independently. The network corresponding to the electrical gap junctional coupling form a small-world network while the connection associated with the chemical synaptic interaction forms a unidirectional random network. Then intralayer connections are allowed to switch stochastically over time with a characteristic rewiring frequency, whereas interlayer connections via electrical synapses are time invariant. We explore the intralayer and interlayer neuronal synchrony in such network and analytically derive the necessary stability conditions for synchrony using master stability function approach, and excellently match with our numerical findings. Interestingly, we find that the higher frequency of switching links in the intralayer enhances both intralayer and interlayer synchrony and conferring larger windows of synchrony. We also analyze the robustness of these synchronization states with respect to initial conditions using the basin stability framework. Furthermore we find that rapidly changing networks take much less time to reach synchronization state. Lastly, we inspect the dynamical robustness of interlayer synchronization against stochastic demultiplexing of each replica, with analytical justification. [ABSTRACT FROM AUTHOR]

Deterioration in dynamical activities may come up naturally or due to environmental influences in a massive portion of biological and physical systems. Such dynamical degradation may have outright effect on the substantive network performance. This requires us to provide some proper prescriptions to overcome undesired circumstances. In this paper, we present a scheme based on external feedback that can efficiently revive dynamism in damaged networks of active and inactive oscillators and thus enhance the network survivability. Both numerical and analytical investigations are performed in order to verify our claim. We also provide a comparative study on the effectiveness of this mechanism for feedbacks to the inactive group or to the active group only. Most importantly, resurrection of dynamical activity is realized even in time-delayed damaged networks, which are considered to be less persistent against deterioration in the form of inactivity in the oscillators. Furthermore, prominence in our approach is substantiated by providing evidence of enhanced network persistence in complex network topologies taking small-world and scale-free architectures, which makes the proposed remedy quite general. Besides the study in the network of Stuart-Landau oscillators, affirmative influence of external feedback has been justified in the network of chaotic Rössler systems as well. [ABSTRACT FROM AUTHOR]

We study synchronization of dynamical systems coupled in time-varying network architectures, composed of two or more network topologies, corresponding to different interaction schemes. As a representative example of this class of time-varying hypernetworks, we consider coupled Hindmarsh-Rose neurons, involving two distinct types of networks, mimicking interactions that occur through the electrical gap junctions and the chemical synapses. Specifically, we consider the connections corresponding to the electrical gap junctions to form a small-world network, while the chemical synaptic interactions form a unidirectional random network. Further, all the connections in the hypernetwork are allowed to change in time, modeling a more realistic neurobiological scenario. We model this time variation by rewiring the links stochastically with a characteristic rewiring frequency ƒ. We find that the coupling strength necessary to achieve complete neuronal synchrony is lower when the links are switched rapidly. Further, the average time required to reach the synchronized state decreases as synaptic coupling strength and/or rewiring frequency increases. To quantify the local stability of complete synchronous state we use the Master Stability Function approach, and for global stability we employ the concept of basin stability. The analytically derived necessary condition for synchrony is in excellent agreement with numerical results. Further we investigate the resilience of the synchronous states with respect to increasing network size, and we find that synchrony can be maintained up to larger network sizes by increasing either synaptic strength or rewiring frequency. Last, we find that time-varying links not only promote complete synchronization, but also have the capacity to change the local dynamics of each single neuron. Specifically, in a window of rewiring frequency and synaptic coupling strength, we observe that the spiking behavior becomes more regular. [ABSTRACT FROM AUTHOR]

We investigate a low-dimensional slow-fast model to understand the dynamical origin of El Niño southern oscillation. A close inspection of the system dynamics using several bifurcation plots reveals that a sudden large expansion of the attractor occurs at a critical system parameter via a type of interior crisis. This interior crisis evolves through merging of a cascade of period-doubling and period-adding bifurcations that leads to the origin of occasional amplitude-modulated extremely large events. More categorically, a situation similar to homoclinic chaos arises near the critical point; however, atypical global instability evolves as a channellike structure in phase space of the system that modulates variability of amplitude and return time of the occasional large events and makes a difference from the homoclinic chaos. The slow-fast timescale of the low-dimensional model plays an important role on the onset of occasional extremely large events. Such extreme events are characterized by their heights when they exceed a threshold level measured by a mean-excess function. The probability density of events' height displays multimodal distribution with an upper-bounded tail. We identify the dependence structure of interevent intervals to understand the predictability of return time of such extreme events using autoregressive integrated moving average model and box-plot analysis. [ABSTRACT FROM AUTHOR]

Chimera states have been a vibrant subject of research in the recent past, but the analytical treatment of transitions from chimeras to coherent states remains a challenge. Here we analytically derive the necessary conditions for this transition by means of the coherent stability function approach, which is akin to the master stability function approach that is traditionally used to study the stability of synchronization in coupled oscillators. In chimera states, there is typically at least one group of oscillators that evolves in a drifting, random manner, while other groups of oscillators follow a smoother, more coherent profile. In the coherent state, there thus exists a smooth functional relationship between the oscillators. This lays the foundation for the coherent stability function approach, where we determine the stability of the coherent state. We subsequently test the analytical prediction numerically by calculating the strength of incoherence during the transition point. We use leech neurons, which exhibit a coexistence of chaotic and periodic tonic spiking depending on initial conditions, coupled via nonlocal electrical synapses, to demonstrate our approach. We systematically explore various dynamical states with the focus on the transitions between chimeras and coherence, fully confirming the validity of the coherent stability function. We also observe complete synchronization for higher values of the coupling strength, which we verify by the master stability function approach. [ABSTRACT FROM AUTHOR]

Chimera state is defined as a mixed type of collective state in which synchronized and desynchronized subpopulations of a network of coupled oscillators coexist and the appearance of such anomalous behavior has strong connection to diverse neuronal developments. Most of the previous studies on chimera states are not extensively done in two-dimensional ensembles of coupled oscillators by taking neuronal systems with nonlinear coupling function into account while such ensembles of oscillators are more realistic from a neurobiological point of view. In this paper, we report the emergence and existence of chimera states by considering locally coupled two-dimensional networks of identical oscillators where each node is interacting through nonlinear coupling function. This is in contrast with the existence of chimera states in two-dimensional nonlocally coupled oscillators with rectangular kernel in the coupling function. We find that the presence of nonlinearity in the coupling function plays a key role to produce chimera states in two-dimensional locally coupled oscillators. We analytically verify explicitly in the case of a network of coupled Stuart-Landau oscillators in two dimensions that the obtained results using Ott-Antonsen approach and our analytical finding very well matches with the numerical results. Next, we consider another type of important nonlinear coupling function which exists in neuronal systems, namely chemical synaptic function, through which the nearest-neighbor (locally coupled) neurons interact with each other. It is shown that such synaptic interacting function promotes the emergence of chimera states in two-dimensional lattices of locally coupled neuronal oscillators. In numerical simulations, we consider two paradigmatic neuronal oscillators, namely Hindmarsh-Rose neuron model and Rulkov map for each node which exhibit bursting dynamics. By associating various spatiotemporal behaviors and snapshots at particular times, we study the chimera states in detail over a large range of coupling parameter. The existence of chimera states is confirmed by instantaneous angular frequency, order parameter and strength of incoherence. [ABSTRACT FROM AUTHOR]

A large class of engineered and natural systems, ranging from transportation networks to neuronal networks, are best represented by multiplex network architectures, namely a network composed of two or more different layers where the mutual interaction in each layer may differ from other layers. Here we consider a multiplex network where the intralayer coupling interactions are switched stochastically with a characteristic frequency. We explore the intralayer and interlayer synchronization of such a time-varying multiplex network. We find that the analytically derived necessary condition for intralayer and interlayer synchronization, obtained by the master stability function approach, is in excellent agreement with our numerical results. Interestingly, we clearly find that the higher frequency of switching links in the layers enhances both intralayer and interlayer synchrony, yielding larger windows of synchronization. Further, we quantify the resilience of synchronous states against random perturbations, using a global stability measure based on the concept of basin stability, and this reveals that intralayer coupling strength is most crucial for determining both intralayer and interlayer synchrony. Lastly, we investigate the robustness of interlayer synchronization against a progressive demultiplexing of the multiplex structure, and we find that for rapid switching of intralayer links, the interlayer synchronization persists even when a large number of interlayer nodes are disconnected. [ABSTRACT FROM AUTHOR]

A metapopulation structure in landscape ecology comprises a group of interacting spatially separated subpopulations or patches of the same species that may experience several local extinctions. This makes the investigation of survivability (in the form of global oscillation) of a metapopulation on top of diverse dispersal topologies extremely crucial. However, among various dispersal topologies in ecological networks, which one can provide higher metapopulation survivability under local extinction is still not well explored. In this article, we scrutinize the robustness of an ecological network consisting of prey-predator patches having Holling type I functional response, against progressively extinct population patches. We present a comprehensive study on this while considering global, small-world, and scale-free dispersal of the subpopulations. Furthermore, we extend our work in enhancing survivability in the form of sustained global oscillation by introducing asymmetries in the dispersal rates of the considered species. Our findings affirm that the asynchrony among the patches plays an important role in the survivability of a metapopulation. In order to demonstrate the model independence of the observed phenomenon, we perform a similar analysis for patches exhibiting Holling type II functional response. On the grounds of the obtained results, our work is expected to provide a better perception of the influence of dispersal arrangements on the global survivability of ecological networks. [ABSTRACT FROM AUTHOR]

We study excitation and suppression of chimera states in an ensemble of nonlocally coupled oscillators arranged in a framework of multiplex network. We consider the homogeneous network (all identical oscillators) with different parametric cases and interlayer heterogeneity by introducing parameter mismatch between the layers. We show the feasibility to suppress chimera states in the multiplex network via moderate interlayer interaction between a layer exhibiting chimera state and other layers which are in a coherent or incoherent state. On the contrary, for larger interlayer coupling, we observe the emergence of identical chimera states in both layers which we call an interlayer chimera state. We map the spatiotemporal behavior in a wide range of parameters, varying interlayer coupling strength and phase lag in two and three multiplexing layers. We also prove the emergence of interlayer chimera states in a multiplex network via evaluation of a continuous model. Furthermore, we consider the two-layered network of Hindmarsh-Rose neurons and reveal that in such a system multiplex interaction between layers is capable of exciting not only the synchronous interlayer chimera state but also nonidentical chimera patterns. [ABSTRACT FROM AUTHOR]

We present a formula for determining synchronizability in large, randomized, and weighted simplicial complexes. This formula leverages eigenratios and costs to assess complete synchronizability under diverse network topologies and intensity distributions. We systematically vary coupling strengths (pairwise and three body), degree, and intensity distributions to identify the synchronizability of these simplicial complexes of the identical oscillators with natural coupling. We focus on randomized weighted connections with diffusive couplings and check synchronizability for different cases. For all these scenarios, eigenratios and costs reliably gauge synchronizability, eliminating the need for explicit connectivity matrices and eigenvalue calculations. This efficient approach offers a general formula for manipulating synchronizability in diffusively coupled identical systems with higher-order interactions simply by manipulating degrees, weights, and coupling strengths. We validate our findings with simplicial complexes of Rössler oscillators and confirm that the results are independent of the number of oscillators, connectivity components, and distributions of degrees and intensities. Finally, we validate the theory by considering a real-world connection topology using chaotic Rössler oscillators.

Swarmalators are entities that swarm through space and sync in time and are potentially considered to replicate the complex dynamics of many real-world systems. So far, the internal dynamics of swarmalators have been taken as a phase oscillator inspired by the Kuramoto model. Here we examine the internal dynamics utilizing an amplitude oscillator capable of exhibiting periodic and chaotic behaviors. To incorporate the dual interplay between spatial and internal dynamics, we propose a general model that keeps the properties of swarmalators intact. This adaptation calls for a detailed study, which we present in this paper. We establish our study with the Rössler oscillator by taking parameters from both chaotic and periodic regions. While the periodic oscillator mimics most of the patterns in the previous phase oscillator model, the chaotic oscillator brings some fascinating states.

Ensembles of coupled nonlinear oscillators are a popular paradigm and an ideal benchmark for analyzing complex collective behaviors. The onset of cluster synchronization is found to be at the core of various technological and biological processes. The current literature has investigated cluster synchronization by focusing mostly on the case of attractive coupling among the oscillators. However, the case of two coexisting competing interactions is of practical interest due to their relevance in diverse natural settings, including neuronal networks consisting of excitatory and inhibitory neurons, the coevolving social model with voters of opposite opinions, and ecological plant communities with both facilitation and competition, to name a few. In the present article, we investigate the impact of repulsive spanning trees on cluster formation within a connected network of attractively coupled limit-cycle oscillators. We successfully predict which nodes belong to each cluster and the emergent frustration of the connected networks independent of the particular local dynamics at the network nodes. We also determine local asymptotic stability of the cluster states using an approach based on the formulation of a master stability function. We additionally validate the emergence of solitary states and antisynchronization for some specific choices of spanning trees and networks.

We present a simple model of driven matter in a 1D medium with pinning impurities, applicable to magnetic domains walls, confined colloids, and other systems. We find rich dynamics, including hysteresis, reentrance, quasiperiodicity, and two distinct routes to chaos. In contrast to other minimal models of driven matter, the model is solvable: we derive the full phase diagram for small N, and for large N, we derive expressions for order parameters and several bifurcation curves. The model is also realistic. Its collective states match those seen in the experiments of magnetic domain walls.

Self-organized bistability (SOB) stands as a critical behavior for the systems delicately adjusting themselves to the brink of bistability, characterized by a first-order transition. Its essence lies in the inherent ability of the system to undergo enduring shifts between the coexisting states, achieved through the self-regulation of a controlling parameter. Recently, SOB has been established in a scale-free network as a recurrent transition to a short-living state of global synchronization. Here, we embark on a theoretical exploration that extends the boundaries of the SOB concept on a higher-order network (implicitly embedded microscopically within a simplicial complex) while considering the limitations imposed by coupling constraints. By applying Ott-Antonsen dimensionality reduction in the thermodynamic limit to the higher-order network, we derive SOB requirements under coupling limits that are in good agreement with numerical simulations on systems of finite size. We use continuous synchronization diagrams and statistical data from spontaneous synchronized events to demonstrate the crucial role SOB plays in initiating and terminating temporary synchronized events. We show that under weak-coupling consumption, these spontaneous occurrences closely resemble the statistical traits of the epileptic brain functioning.

In a predator-prey metapopulation, two traits are adversely related: synchronization and persistence. A decrease in synchrony apparently leads to an increase in persistence and, therefore, necessitates the study of desynchrony in a metapopulation. In this article, we study predator-prey patches that communicate with one another while being interconnected through distinct dispersal structures in the layers of a three-layer multiplex network. We investigate the synchronization phenomenon among the patches of the outer layers by introducing higher-order interactions (specifically three-body interactions) in the middle layer. We observe a decrease in the synchronous behavior or, alternatively, an increase in desynchrony due to the inclusion of group interactions among the patches of the middle layer. The advancement of desynchrony becomes more prominent with increasing strength and numbers of three-way interactions in the middle layer. We analytically validate our numerical results by performing a stability analysis of the referred synchronous solution using the master stability function approach. Additionally, we verify our findings by taking into account two distinct predator-prey models and dispersal topologies, which ultimately supports that the findings are generalizable across various models and dispersal structures.

Swarmalators are oscillatory systems endowed with a spatial component, whose spatial and phase dynamics affect each other. Such systems can demonstrate fascinating collective dynamics resembling many real-world processes. Through this work, we study a population of swarmalators where they are divided into different communities. The strengths of spatial attraction, repulsion, as well as phase interaction differ from one group to another. Also, they vary from intercommunity to intracommunity. We encounter, as a result of variation in the phase coupling strength, different routes to achieve the static synchronization state by choosing several parameter combinations. We observe that when the intercommunity phase coupling strength is sufficiently large, swarmalators settle in the static synchronization state. However, with a significant small phase coupling strength the state of antiphase synchronization as well as chimeralike coexistence of sync and async are realized. Apart from rigorous numerical results, we have been successful to provide semianalytical treatment for the existence and stability of global static sync and the antiphase sync states.

With synchronization being one of nature's most ubiquitous collective behaviors, the field of network synchronization has experienced tremendous growth, leading to significant theoretical developments. However, most previous studies consider uniform connection weights and undirected networks with positive coupling. In the present article, we incorporate the asymmetry in a two-layer multiplex network by assigning the ratio of the adjacent nodes' degrees as the weights to the intralayer edges. Despite the presence of degree-biased weighting mechanism and attractive-repulsive coupling strengths, we are able to find the necessary conditions for intralayer synchronization and interlayer antisynchronization and test whether these two macroscopic states can withstand demultiplexing in a network. During the occurrence of these two states, we analytically calculate the oscillator's amplitude. In addition to deriving the local stability conditions for interlayer antisynchronization via the master stability function approach, we also construct a suitable Lyapunov function to determine a sufficient condition for global stability. We provide numerical evidence to show the necessity of negative interlayer coupling strength for the occurrence of antisynchronization, and such repulsive interlayer coupling coefficients cannot destroy intralayer synchronization.

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

A long-standing expectation is that two repulsively coupled oscillators tend to oscillate in opposite directions. It has been difficult to achieve complete synchrony in coupled identical oscillators with purely repulsive coupling. Here, we introduce a general coupling condition based on the linear matrix of dynamical systems for the emergence of the complete synchronization in pure repulsively coupled oscillators. The proposed coupling profiles (coupling matrices) define a bidirectional cross-coupling link that plays the role of indicator for the onset of complete synchrony between identical oscillators. We illustrate the proposed coupling scheme on several paradigmatic two-coupled chaotic oscillators and validate its effectiveness through the linear stability analysis of the synchronous solution based on the master stability function approach. We further demonstrate that the proposed general condition for the selection of coupling profiles to achieve synchronization even works perfectly for a large ensemble of oscillators.

Understanding how the interplay between higher-order and multilayer structures of interconnections influences the synchronization behaviors of dynamical systems is a feasible problem of interest, with possible application in essential topics such as neuronal dynamics. Here, we provide a comprehensive approach for analyzing the stability of the complete synchronization state in simplicial complexes with numerous interaction layers. We show that the synchronization state exists as an invariant solution and derive the necessary condition for a stable synchronization state in the presence of general coupling functions. It generalizes the well-known master stability function scheme to the higher-order structures with multiple interaction layers. We verify our theoretical results by employing them on networks of paradigmatic Rössler oscillators and Sherman neuronal models, and we demonstrate that the presence of group interactions considerably improves the synchronization phenomenon in the multilayer framework.

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

The stability analysis of synchronization patterns on generalized network structures is of immense importance nowadays. In this article, we scrutinize the stability of intralayer synchronous state in temporal multilayer hypernetworks, where each dynamic units in a layer communicate with others through various independent time-varying connection mechanisms. Here, dynamical units within and between layers may be interconnected through arbitrary generic coupling functions. We show that intralayer synchronous state exists as an invariant solution. Using fast-switching stability criteria, we derive the condition for stable coherent state in terms of associated time-averaged network structure, and in some instances we are able to separate the transverse subspace optimally. Using simultaneous block diagonalization of coupling matrices, we derive the synchronization stability condition without considering time-averaged network structure. Finally, we verify our analytically derived results through a series of numerical simulations on synthetic and real-world neuronal networked systems.

A reservoir computing based echo state network (ESN) is used here for the purpose of predicting the spread of a disease. The current infection trends of a disease in some targeted locations are efficiently captured by the ESN when it is fed with the infection data for other locations. The performance of the ESN is first tested with synthetic data generated by numerical simulations of independent uncoupled patches, each governed by the classical susceptible-infected-recovery model for a choice of distributed infection parameters. From a large pool of synthetic data, the ESN predicts the current trend of infection in 5% patches by exploiting the uncorrelated infection trend of 95% patches. The prediction remains consistent for most of the patches for approximately 4 to 5 weeks. The machine's performance is further tested with real data on the current COVID-19 pandemic collected for different countries. We show that our proposed scheme is able to predict the trend of the disease for up to 3 weeks for some targeted locations. An important point is that no detailed information on the epidemiological rate parameters is needed; the success of the machine rather depends on the history of the disease progress represented by the time-evolving data sets of a large number of locations. Finally, we apply a modified version of our proposed scheme for the purpose of future forecasting.

Formation of diverse patterns in spatially extended reaction-diffusion systems is an important aspect of study that is pertinent to many chemical and biological processes. Of special interest is the peculiar phenomenon of chimera state having spatial coexistence of coherent and incoherent dynamics in a system of identically interacting individuals. In the present article, we report the emergence of various collective dynamical patterns while considering a system of prey-predator dynamics in the presence of a two-dimensional diffusive environment. Particularly, we explore the observance of four distinct categories of spatial arrangements among the species, namely, spiral wave, spiral chimera, completely synchronized oscillations, and oscillation death states in a broad region of the diffusion-driven parameter space. Emergence of amplitude-mediated spiral chimera states displaying drifted amplitudes and phases in the incoherent subpopulation is detected for parameter values beyond both Turing and Hopf bifurcations. Transition scenarios among all these distinguishable patterns are numerically demonstrated for a wide range of the diffusion coefficients which reveal that the chimera states arise during the transition from oscillatory to steady-state dynamics. Furthermore, we characterize the occurrence of each of the recognizable patterns by estimating the strength of incoherent subpopulations in the two-dimensional space.

A series of recent publications, within the framework of network science, have focused on the coexistence of mixed attractive and repulsive (excitatory and inhibitory) interactions among the units within the same system, motivated by the analogies with spin glasses as well as to neural networks, or ecological systems. However, most of these investigations have been restricted to single layer networks, requiring further analysis of the complex dynamics and particular equilibrium states that emerge in multilayer configurations. This article investigates the synchronization properties of dynamical systems connected through multiplex architectures in the presence of attractive intralayer and repulsive interlayer connections. This setting enables the emergence of antisynchronization, i.e., intralayer synchronization coexisting with antiphase dynamics between coupled systems of different layers. We demonstrate the existence of a transition from interlayer antisynchronization to antiphase synchrony in any connected bipartite multiplex architecture when the repulsive coupling is introduced through any spanning tree of a single layer. We identify, analytically, the required graph topologies for interlayer antisynchronization and its interplay with intralayer and antiphase synchronization. Next, we analytically derive the invariance of intralayer synchronization manifold and calculate the attractor size of each oscillator exhibiting interlayer antisynchronization together with intralayer synchronization. The necessary conditions for the existence of interlayer antisynchronization along with intralayer synchronization are given and numerically validated by considering Stuart-Landau oscillators. Finally, we also analytically derive the local stability condition of the interlayer antisynchronization state using the master stability function approach.

We investigate the impact of attractive-repulsive interaction in networks of limit cycle oscillators. Mainly we focus on the design principle for generating an antiphase state between adjacent nodes in a complex network. We establish that a partial negative control throughout the branches of a spanning tree inside the positively coupled limit cycle oscillators works efficiently well in comparison with randomly chosen negative links to establish zero frustration (antiphase synchronization) in bipartite graphs. Based on the emergence of zero frustration, we develop a universal 0-π rule to understand the antiphase synchronization in a bipartite graph. Further, this rule is used to construct a nonbipartite graph for a given nonzero frustrated value. We finally show the generality of 0-π rule by implementing it in arbitrary undirected nonbipartite graphs of attractive-repulsively coupled limit cycle oscillators and successfully calculate the nonzero frustration value, which matches with numerical data. The validation of the rule is checked through the bifurcation analysis of small networks. Our work may unveil the underlying mechanism of several synchronization phenomena that exist in a network of oscillators having a mixed type of coupling.

Chaos-synchronization-based multiparameter estimation of a multiply delayed feedback system is investigated. We propose an adaptive method that can estimate all the parameters of the response system using the driving signal only. In the past few years, various methods have been developed for estimation of multiparameters of a chaotic system but most of them require more than one time series to estimate all the parameters of a chaotic or hyperchaotic system. The proposed method requires only a single chaotic time series to estimate all the parameters. A sufficient condition for synchronization is derived and it is shown that the numerical results well support the analytic calculations. The synchronized system has applications in cryptographic encoding for digital and analog signals, which is shown with an example.