[en] Synchronization is one of important collective behaviors in various systems. The identification of different synchronous dynamics and types of transition between different dynamical states has drawn great interests. In this work, we study Kuramoto model in the presence of correlation between coupling strength and natural frequency. By manipulating the correlation between coupling strength and natural frequency, synchronization transition can either be the continuous type or the discontinuous one. Rich synchronous dynamics and different transitions between them can be realized by manipulating the correlation. We hope that the coupled systems with correlation between coupling strength and natural frequency could provide a general platform to investigate synchronous dynamics.

[en] Continuous energy pumping and exchange along the coupling channel can balance the energy release between nonlinear oscillators for reaching complete synchronisation. When external stimulus is applied, energy is injected and encoded for regulating the dynamics of nonlinear oscillators and circuits. In this paper, the synchronisation between memristive Rössler oscillators is investigated by reactivating one memristive variable,and external stimuli are changed to detect the occurrence of synchronisation without direct variable coupling. In the presence of periodical stimulus, stochastic switch and feedback on the memristive variable can induce synchronisation between two memristive oscillators and chain network composed of memristive oscillators. In the presence of noise, stochastic feedback and disturbance on the memristive variable can keep synchronisation stable between two oscillators, and complete synchronisation is realised. In addition, the synchronisation factor and spatial patterns are calculated to confirm the occurrence of synchronisation between more chaotic oscillators when memristive function is activated even when no coupling channels are switched on. (author)

[en] The synchronization and asynchronization of two coupled excitable systems are investigated. The two systems with different initial configurations, which are separately a single spiral wave (or a travel wave) and the rest state, can be developed to the synchronizing state with the same spiral wave (or travel wave) in each system, when the coupling is very strong. Decreasing the coupling intensity, two rest states or two different configurations appear in the two systems. The qualitative analysis and interpretation are given.

[en] In this paper some simple models of coupled oscillators are defined. They are used as tools to analyze properties of synchronization domains. It is possible to get the general organization of these domains (generally known as tongues), particularly when the coupling or the forcing signal is 'square'. At large forcing a phenomenon, very similar to the ratchet wheel mechanism, takes place and many synchronization domains disappear. Generally the tongue associated with the relative winding number 1/1 becomes predominant and only tongues with relative winding number p/q < 1 remain. This phenomenon is rather general and appears in many real situations. It is related with motion and transport in physical and biological sciences.

[en] We present and analyze a nonabelian version of the Kuramoto system, which we call the Quantum Kuramoto system. We study the stability of several classes of special solutions to this system, and show that for certain connection topologies the system supports multiple attractors. We also present estimates on the maximal possible heterogeneity in this system that can support an attractor, and study the effect of modifications analogous to phase-lag.

[en] A recent study has found an explosive synchronization in a Kurammoto model on scale-free networks when the natural frequencies of oscillators are equal to their degrees. In this work, we introduce a quantity to characterize the correlation between the structural and the dynamical properties and investigate the impacts of the correlation on the synchronization transition in the Kuramoto model on scale-free networks. We find that the synchronization transition may be either a continuous one or a discontinuous one depending on the correlation and that strong correlation always postpones both the transitions from the incoherent state to a synchronous one and the transition from a synchronous state to the incoherent one. We find that the dependence of the synchronization transition on the correlation is also valid for other types of distributions of natural frequency. (general)

[en] The Kuramoto model for an ensemble of coupled oscillators provides a paradigmatic example of non-equilibrium transitions between an incoherent and a synchronized state. A frequency-weighted network of Kuramoto oscillators is proposed, where the oscillators are asymmetrically coupled with the weights depending on their own native frequencies. Moreover, the characteristics of the whole network can be described by a single weighting exponent β. To obtain some analytical results, we focus on three special values of the weighting exponent β. Obviously, the network of oscillators in connection with the heterogeneous coupling scheme turns out to exhibit richer dynamics. Our findings indicate that the weighting exponents should be of importance to affect the network's synchronization ability. (paper)

[en] A new synchronization method is investigated for node of complex networks consists of complex chaotic system. When complex networks realize synchronization, different component of complex state variable synchronize up to different scaling complex function by a designed complex feedback controller. This paper change synchronization scaling function from real field to complex field for synchronization in node of complex networks with complex chaotic system. Synchronization in constant delay and time-varying coupling delay complex networks are investigated, respectively. Numerical simulations are provided to show the effectiveness of the proposed method

[en] We have observed anti-synchronization phenomena in different chaotic dynamical systems. Anti-synchronization can be characterized by the vanishing of the sum of relevant variables. Anti-synchronization problem for different chaotic dynamical systems with fully unknown parameters in response system is analyzed. This technique is applied to achieve anti-synchronization between Lorenz system, Lue system and Four-scroll system. Numerical simulations are provided to verify the effectiveness of the proposed methods.

[en] The roles played by drive and response systems on generalized chaos synchronization (GS) are studied. And the generalized synchronization is classified, based on these roles, to three distinctive types: the passive GS which is mainly determined by the response system and insensitive to the driving signal; the resonant GS where phase synchronization between the drive and response systems is preceding GS; and the interacting GS where both the drive and response have influences on the status of GS. The features of these GS types and the possible changes from one types to others are investigated