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We consider networks of coupled stochastic oscillators. When coupled we find strong collective oscillations, while each unit remains stochastic. In the limit (N\to \infty) we derive a system of integro-delay equations and show analytically…
We investigate synchronization in the presence of delay time modulation for application to communication. We have observed that the robust synchronization is established by a common delay signal and its threshold is presented using Lyapunov…
A scenario has recently been reported in which in order to stabilize complete synchronization of an oscillator network---a symmetric state---the symmetry of the system itself has to be broken by making the oscillators nonidentical. But how…
Many network applications rely on the synchronization of coupled oscillators. For example, such synchronization can provide networked devices with a common temporal reference necessary for coordinating actions or decoding transmitted…
We study control of synchronization in weakly coupled oscillator networks by using a phase reduction approach. Starting from a general class of limit cycle oscillators we derive a phase model, which shows that delayed feedback control…
In this paper, we use dynamical systems to analyze stability of desynchronization algorithms at equilibrium. We start by illustrating the equilibrium of a dynamic systems and formalizing force components and time phases. Then, we use Linear…
We give a succinct and self-contained description of the synchronized motion on networks of mutually coupled oscillators. Usually, the stability criterion for the stability of synchronized motion is obtained in terms of Lyapunov exponents.…
Linear stability of synchronized states in networks of delay-coupled oscillators depends on the type of interaction, the network and oscillator properties. For inert oscillator response, found ubiquitously from biology to engineering,…
We study the synchronization phenomena in a system of globally coupled oscillators with time delay in the coupling. The self-consistency equations for the order parameter are derived, which depend explicitly on the amount of delay. Analysis…
It is widely assumed that neural activity related to synchronous rhythms of large portions of neurons in specific locations of the brain is responsible for the pathology manifested in patients' uncontrolled tremor and other similar…
Suppose we are given a system of coupled oscillators on an unknown graph along with the trajectory of the system during some period. Can we predict whether the system will eventually synchronize? Even with a known underlying graph…
This letter investigates the problem of output synchronisation in heterogeneous dynamical networks with nonlinear diffusive couplings in the presence of disturbances on the coupling links. By exploiting relative dissipativity properties…
We introduce a novel concept of generalized synchronization, able to encompass the setting of collective synchronized behavior for mutually coupled systems and networking systems featuring complex topologies in their connections. The onset…
We study two delay-coupled FitzHugh-Nagumo systems, introducing a mismatch between the delay times, as the simplest representation of interacting neurons. We demonstrate that the presence of delays can cause periodic oscillations which…
Synchronization in coupled oscillators networks is a remarkable phenomenon of relevance in numerous fields. For Kuramoto oscillators the loss of synchronization is determined by a trade-off between coupling strength and oscillator…
Oscillators coupled in a network can synchronize with each other to yield a coherent population rhythm. If multiple such networks are coupled together, the question arises whether these rhythms will synchronize. We investigate the impact of…
In this paper, we study synchronization in the delayed discrete-time complex networks. Several criterions of synchronization stability for such networks are established. And illustrative examples are presented. The numerical simulations…
Synchronization is essential for the operation of AC power systems: All generators in the power grid must rotate with fixed relative phases to enable a steady flow of electric power. Understanding the conditions for and the limitations of…
Cluster synchronization is a phenomenon in which oscillators in a given network are partitioned into synchronous clusters. As recently shown, diverse cluster synchronization patterns can be found using network symmetry when the oscillators…
Synchronization of chaotic units coupled by their time delayed variables are investigated analytically. A new type of cooperative behavior is found: sublattice synchronization. Although the units of one sublattice are not directly coupled…