Related papers: Delayed Self-Synchronization in Homoclinic Chaos
We consider a network of identical pulse-coupled oscillators with delay and all-to-all coupling. We demonstrate that the discontinuous nature of the dynamics induces the appearance of isochronous regions---subsets of the phase space filled…
We explore the behaviour of an ensemble of chaotic oscillators coupled only to an external chaotic system, whose intrinsic dynamics may be similar or dissimilar to the group. Counter-intuitively, we find that a dissimilar external system…
Numerical experiments recently discussed in the literature show that identical nonlinear chaotic systems linked by a common noise term (or signal) may synchronize after a finite time. We study the process of synchronization as function of…
Exploring continuous time crystals (CTCs) within the symmetric subspace of spin systems has been a subject of intensive research in recent times. Thus far, the stability of the time-crystal phase outside the symmetric subspace in such spin…
Homoclinic and heteroclinic orbits provide a skeleton of the full dynamics of a chaotic dynamical system and are the foundation of semiclassical sums for quantum wave packet, coherent state, and transport quantities. Here, the homoclinic…
We study experimentally the synchronization patterns in time-delayed directed Boolean networks of excitable systems. We observe a transition in the network dynamics when the refractory time of the individual systems is adjusted. When the…
In this paper, stability analysis of time delay systems is considered based on decomposition of the systems to subsystems. The decomposition process needs matrices of these systems to be simultaneously block triangularize. We show that a…
The dynamics of an ensemble of bistable elements with global time-delayed coupling under the influence of noise is studied analytically and numerically. Depending on the noise level the system undergoes ordering transitions and demonstrates…
We show that two initially weakly coupled chaotic systems can achieve self-organized synchronization by adaptively reducing their speed and/or enhancing the coupling strength. Explicit adaptive algorithms for speed-reduction and…
Real-world systems can be strongly influenced by time delays occurring in self-coupling interactions, due to unavoidable finite signal propagation velocities. When the delays become significantly long, complicated high-dimensional phenomena…
We study chaotic systems with multiple time delays that range over several orders of magnitude. We show that the spectrum of Lyapunov exponents (LE) in such systems possesses a hierarchical structure, with different parts scaling with the…
We study synchronisation between periodically driven, interacting classical spins undergoing a Hamiltonian dynamics. In the thermodynamic limit there is a transition between a regime where all the spins oscillate synchronously for an…
We study a system of four identical globally coupled phase oscillators with biharmonic coupling function. Its dimension and the type of coupling make it the minimal system of Kuramoto-type (both in the sense of the phase space's dimension…
Occurrence of strong or mass synchronization of a large number of neuronal populations in the brain characterizes its pathological states. In order to establish an understanding of the mechanism underlying such pathological synchronization…
In this work, inspired in the symbolic dynamic of chaotic systems and using machine learning techniques, a control strategy for complex systems is designed. Unlike the usual methodologies based on modeling, where the control signal is…
Dissipation is commonly regarded as an obstacle to quantum control, as it induces decoherence and irreversibility. Here we demonstrate that dissipation can instead be exploited as a resource to reshape the dynamics of interacting quantum…
The behaviors of coupled chaotic oscillators before complete synchronization were investigated. We report three phenomena: (1) The emergence of long-time residence of trajectories besides one of the saddle foci; (2) The tendency that orbits…
We study the effect of a time-delayed feedback within a generic model for a saddle-node bifurcation on a limit cycle. Without delay the only attractor below this global bifurcation is a stable node. Delay renders the phase space…
This paper deals with adaptive synchronization of chaos in the presence of time-varying communication-delays. We consider two bidirectionally coupled systems that seek to synchronize through a signal that each system sends to the other one…
Dynamical networks are important models for the behaviour of complex systems, modelling physical, biological and societal systems, including the brain, food webs, epidemic disease in populations, power grids and many other. Such dynamical…