The model of nonlocally coupled identical phase oscillators on complex networks is investigated. We find the existence chimera states in which evolve into distinct coherent and incoherent groups. that group always contains same no matter what initial conditions are. properties their dependence parameters are investigated both scale-free Erd\"os-R\'enyi networks.

Collective ordering behaviors are typical macroscopic manifestations embedded in complex systems and can be ubiquitously observed across various physical backgrounds. Elements may self-organize via mutual or external couplings to achieve diverse spatiotemporal coordinations. The order parameter, as a powerful quantity describing the transition collective states, emerge spontaneously from large numbers of degrees freedom through competitions. In this minireview, we extensively discussed...

The behaviors of coupled oscillators, each which has periodic motion with random natural frequency in the absence coupling, are investigated. Some novel collective phenomena revealed. At onset instability phase-locking state, simultaneous phase slips all oscillators and quantized shifts these observed. By increasing a bifurcation tree from high-dimensional quasiperiodicity to chaos periodicity is found. Different orders synchronizations chaotic clusters play key role for constructing this structure.

The relation between generalized synchronization and phase is investigated. It was claimed that always leads to synchronization, a weaker form than synchronization. We propose examples can be depending on parameter misfits. Moreover, does not lead

Abstract An interesting alternate attractor chimeralike state can self-organize to emerge on rings of chaotic Lorenz-type oscillators. The local dynamics any two neighboring oscillators spontaneously change from the butterfly-like attractors symmetric and converse ones, which forms ring. This is distinctly different traditional chimera states with unique attractor. effective driven-oscillator approach proposed reveal mechanism in forming this new oscillation mode predict critical coupling...

The remarkable phenomenon of chimera state in systems non-locally coupled, identical oscillators has attracted a great deal recent theoretical and experimental interests. In such state, different groups can exhibit characteristically distinct types dynamical behaviors, spite identity the oscillators. But how robust are states against random perturbations to structure underlying network? We address this fundamental issue by studying effects removal links on probability for states. Using...

The adaptation underlying many realistic processes plays a pivotal role in shaping the collective dynamics of diverse systems. Here, we untangle generic conditions for synchronization transitions system coupled phase oscillators incorporating adaptive scheme encoded by feedback between coupling and order parameter via power-law function with different weights. We mathematically argue that, subcritical supercritical correlation scenarios, there exists no critical fraction converting from...

In this paper, a novel fractional-order chaotic system equipped with symmetric attractors was proposed for the full-coverage path-planning problem of mobile robots, especially in application scenarios where path privacy needs to be protected. By coupling kinematic model robot, algorithm designed realize encrypted planning. A predefined time-synchronization control strategy effectively resolved inconsistencies caused by initial position, time delay, and uncertain disturbances. Numerical...

Chaos should occur often in gene regulatory networks (GRNs) which have been widely described by nonlinear coupled ordinary differential equations, if their dimensions are no less than 3. It is therefore puzzling that chaos has never reported GRNs nature and also extremely rare models of GRNs. On the other hand, topic motifs attracted great attention studying biological networks, network suggested to be elementary building blocks carry out some key functions network. In this paper, chaotic...

Nowadays, massive amounts of data are available for analysis in natural and social systems the tasks to depict system structures from data, i.e., inverse problems, become one central issues wide interdisciplinary fields. In this paper, we study problem dynamic complex networks driven by white noise. A simple universal inference formula double correlation matrices noise-decorrelation (DCMND) method is derived analytically, numerical simulations confirm that DCMND can accurately both network...

Abstract Abrupt and continuous spontaneous emergence of collective synchronization coupled oscillators have attracted much attention. In this paper, we propose a dynamical ensemble order parameter equation that enables us to grasp the essential low-dimensional mechanism in networks oscillators. Different solutions build correspondences with diverse states different bifurcations reveal various transitions among these states. The structural relationship between incoherent state synchronous...

In this paper, we propose a retrospective and summary on recent studies of chimera states. Chimera states demonstrate striking inhomogeneous spatiotemporal patterns emerging in homogeneous systems through unexpected spontaneous symmetry breaking, where the consequent are composed both coherence incoherence domains, respectively characterized by synchronized desynchronized motions oscillators. Since discovery Kuramoto others, collective behavior has attracted great deal research interest...

We unveil the basic mechanisms and general conditions for emergence of Bellerophon states, which are higher order coherent states appearing in globally coupled phase oscillators. The critical points involved transitions determined analytically. significant feature is that oscillators' effective frequencies locked to quantized plateaus, a point fully clarified on basis circle map theory. Each plateau corresponds harmonic frequency Fourier decomposition parameter. Our approach exploits fact...

Many networked systems display some kind of dynamics behaving in a style with both continuous and impulsive communications. The cooperation behaviors these connected or topologies communications are important to understand. This paper is devoted the synchronization system hybrid communications, where each topology communication mode not every moment. Two structures, i.e., fixed structure switching taken into consideration. A general concept directed spanning tree (DST) proposed describe...

Generalized synchronization in an array of mutually (bidirectionally) coupled nonidentical chaotic oscillators is studied. Coupled Lorenz and Lorenz-Rossler are adopted as our working models. With increasing the coupling strengths, system experiences a cascade transitions from partial to global generalized synchronizations, i.e., different gradually entrained through clustering process. This scenario reveals intrinsic self-organized order groups interacting units, which generalizes idea...

Heterogeneous coupling patterns among interacting elements are ubiquitous in real systems ranging from physics, chemistry to biology communities, which have attracted much attention during recent years. In this paper, we extend the Kuramoto model by considering a particular heterogeneous scheme an ensemble of phase oscillators, where each oscillator pair interacts with different strength that is weighted general function natural frequency. The theory for transition synchronization can be...

Abstract We reveal a class of universal phase transitions to synchronization in Kuramoto-like models with both in- and out-coupling heterogeneity. By analogy metastable states, an oscillatory state occurs as high-order coherent accompanying explosive the system. The critical points transition stationary solutions are obtained analytically, by use mean-field theory. In particular, stable conditions for emergence phase-locked states determined consistently analysis based on Ott–Antonsen...

The optimization of synchronization on distributed power grids is an important topic in recent years. We extensively study the by restructuring grid topology terms connection rewirings. Due to node-link dual property networks, i.e., intrinsic generator-load dynamics nodes and multiple-attribute connections, we propose frequency-correlation-optimization scheme get with largest anti-correlation targeting frequency-correlation function among nodes. optimizations both sparse dense networks are...

Directed collective motion in a circular array of unidirectionally coupled oscillators with symmetric potential is obtained numerically the absence external bias. This striking feature interpreted as effect spontaneous breaking temporal symmetry coupling. It revealed that proper match various control parameters important generating an optimal coherent global transport. Noise-sustained directed transport also observed, and related stochastic resonance autonomous system identified.

Abstract Recently, the first-order synchronization transition has been studied in systems of coupled phase oscillators. In this paper, we propose a framework to investigate frequency-weighted Kuramoto model with all-to-all couplings. A rigorous mean-field analysis is implemented predict possible steady states. Furthermore, detailed linear stability proves that incoherent state only neutrally stable below threshold. Nevertheless, interestingly, amplitude order parameter decays exponentially...

We fully describe the mechanisms underlying synchronization in starlike networks of phase oscillators. In particular, routes to and critical points for associated transitions are determined analytically. contrast classical Kuramoto theory, we unveil that relaxation rates each equilibrium state indeed exist remain invariant under three levels descriptions corresponding different geometric implications. The special symmetry coupling determines a quasi-Hamiltonian property, which is further...

Many-body interactions between dynamical agents have caught particular attention in recent works that found wide applications physics, neuroscience, and sociology. In this paper we investigate such higher order (nonadditive) on collective dynamics a system of globally coupled heterogeneous phase oscillators. We show the three-body encoded microscopically nonlinear couplings give rise to added dynamic phenomena occurring beyond pairwise interactions. The general displays an abrupt...