Related papers: Periodic systems have new classes of synchronizati…
Empirical diagnosis of stability has received considerable attention, mostly focused on variance metrics for early warning signals of abrupt system change. Despite this, the theoretical foundation and application has been limited to…
Synchrony is one of the most common dynamical states emerging on networks. The speed of convergence towards synchrony provides a fundamental collective time scale for synchronizing systems. Here we study the asymptotic synchronization times…
This work studies the stabilization for a periodic parabolic system under perturbations in the system conductivity. A perturbed system does not have any periodic solution in general. However, we will prove that the perturbed system can…
We uncover and characterize different chaotic transport scenarios on perfect periodic surfaces by controlling the chaotic dynamics of particles subjected to periodic external forces in the absence of a ratchet effect. After identifying…
The stable functionality of networked systems is a hallmark of their natural ability to coordinate between their multiple interacting components. Yet, strikingly, real-world networks seem random and highly irregular, apparently lacking any…
There are many natural, physical, and biological systems that exhibit multiple time scales. For example, the dynamics of a population of ticks can be described in continuous time during their individual life cycle yet discrete time is used…
Dynamical behaviour of discrete dynamical systems has been investigated extensively in the past few decades. However, in several applications, long term memory plays an important role in the evolution of dynamical variables. The definition…
Characterization of classes of switching signals that ensure stability of switched systems occupies a significant portion of the switched systems literature. This article collects a multitude of stabilizing switching signals under an…
This article provides a self-contained comprehensive review of the phenomenon of synchronization in dynamical systems, with a particular focus on chaotic systems in both continuous-time and discrete-time contexts. Synchronization, initially…
The master equation plays an important role in many scientific fields including physics, chemistry, systems biology, physical finance, and sociodynamics. We consider the master equation with periodic transition rates. This may represent an…
A new measure to characterize stability of complex dynamical systems against large perturbation is suggested, the stability threshold (ST). It quantifies the magnitude of the weakest perturbation capable to disrupt the system and switch it…
The (non-initialized, non-deterministic) asynchronous systems (in the input-output sense) are multi-valued functions from m-dimensional signals to sets of n-dimensional signals, the concept being inspired by the modeling of the asynchronous…
Chaos is an active research subject in the fields of science in recent years. it is a complex and an erratic behavior that is possible in very simple systems. in the present day, the chaotic behavior can be observed in experiments. Many…
The paper deals with the convergence properties of the products of random (row-)stochastic matrices. The limiting behavior of such products is studied from a dynamical system point of view. In particular, by appropriately defining a dynamic…
We investigate the connection between the dynamics of synchronization and the modularity on complex networks. Simulating the Kuramoto's model in complex networks we determine patterns of meta-stability and calculate the modularity of the…
The apparent stability of population oscillations in ecological systems is a long-standing puzzle. A generic solution for this problem is suggested here. The stabilizing mechanism involves the combined effect of spatial migration,…
We apply the phase-reduction analysis to examine synchronization properties of periodic fluid flows. The dynamics of unsteady flows are described in terms of the phase dynamics reducing the high-dimensional fluid flow to its single scalar…
We adapt a previous model and analysis method (the {\it master stability function}), extensively used for studying the stability of the synchronous state of networks of identical chaotic oscillators, to the case of oscillators that are…
In the realm of spatiotemporal chaos, unstable periodic orbits play a major role in understanding the dynamics. Their stability changes and bifurcations in general are thus of central interest. Here, coupled map lattice discretizations of…
The searching for the stable patterns in the evolution of cellular automata is implemented using stochastic synchronization between the present structures of the system and its precedent configurations. For most of the known evolution rules…