Related papers: Unstable attractors induce perpetual synchronizati…
In this paper an approach to generate hidden attractors based on piecewise linear (PWL) systems is studied. The approach consists of the coexistence of self-excited attrators and hidden attractors, i.e., the equilibria of the system are…
Cluster synchronization in networks of coupled oscillators is the subject of broad interest from the scientific community, with applications ranging from neural to social and animal networks and technological systems. Most of these networks…
We study transient sequential dynamics of evolving dynamical networks, i.e., those having active nodes and links and activity-dependent topology. We show that such networks can generate sequences of metastable cluster states where each…
Synchronization is a universal phenomenon found in many non-equilibrium systems. Much recent interest in this area has overlapped with the study of complex networks, where a major focus is determining how a system's connectivity patterns…
Nonlinear oscillators can mutually synchronize when they are driven by common external impulses. Two important scenarios are (i) synchronization resulting from phase locking of each oscillator to regular periodic impulses and (ii)…
Collective behavior in large ensembles of dynamical units with non-pairwise interactions may play an important role in several systems ranging from brain function to social networks. Despite recent work pointing to simplicial structure,…
We consider a system of two identical linearly coupled Lorenz oscillators, presenting synchro- nization of chaotic motion for a specified range of the coupling strength. We verify the existence of global synchronization and…
We investigate the combined effects of distributed delay and the balance between excitatory and inhibitory nodes on the stability of synchronous oscillations in a network of coupled Stuart--Landau oscillators. To this end a network model is…
We study synchronization of nonlinear systems that satisfy an incremental passivity property. We consider the case where the control input is subject to a class of disturbances, including constant and sinusoidal disturbances with unknown…
We study synchronization dynamics in populations of coupled phase oscillators with higher-order interactions and community structure. We find that the combination of these two properties gives rise to a number of states unsupported by…
Research on synchronization of coupled oscillators has helped explain how uniform behavior emerges in populations of non-uniform systems. But explaining how uniform populations engage in sustainable non-uniform synchronization may prove to…
Continuous attractor neural networks generate a set of smoothly connected attractor states. In memory systems of the brain, these attractor states may represent continuous pieces of information such as spatial locations and head directions…
A universal mechanism underlying generalized synchronization conditions in unidirectionally coupled stochastic oscillators is considered. The consideration is carried out in the framework of a modified system with additional dissipation.…
This work explores a synchronization-like phenomenon induced by common noise for continuous-time Markov jump processes given by chemical reaction networks. A corresponding random dynamical system is formulated in a two-step procedure, at…
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…
Attractors of dynamical systems may be networks in phase space that can be heteroclinic (where there are dynamical connections between simple invariant sets) or excitable (where a perturbation threshold needs to be crossed to a dynamical…
Non-reciprocal couplings are frequently found in systems out-of-equilibrium such as neuronal networks. We consider generalized Kuramoto models with non-reciprocal adaptive couplings. The non-reciprocity refers to the type of couplings…
The property of desynchronization in an all-to-all network of homogeneous impulse-coupled oscillators is studied. Each impulse-coupled oscillator is modeled as a hybrid system with a single timer state that self-resets to zero when it…
In past works, various schemes for adaptive synchronization of chaotic systems have been proposed. The stability of such schemes is central to their utilization. As an example addressing this issue, we consider a recently proposed adaptive…
We investigate the impact of bistability in the emergence of synchronization in networks of chaotic maps with delayed coupling. The existence of a single finite attractor of the uncoupled map is found to be responsible for the emergence of…