Related papers: Necessary and Sufficient Conditions for Stable Syn…
During the past decades, the question of existence and properties of a random attractor of a random dynamical system generated by an S(P)DE has received considerable attention, for example by the work of Gess and R\"ockner. Recently some…
Synchronization of chaotic system may occur only when the largest conditional Lyapunov exponent of the driven system is negative. The synchronization with positive conditional Lyapunov reported in a recent paper (Phys. Rev. E, {\bf 56},…
This article aims to investigate sufficient conditions for the stability of stochastic differential equations with a random structure, particularly in contexts involving the presence of concentration points. The proof of asymptotic…
A one-dimensional chain of sporadic maps with asymmetric nearest neighbour couplings is numerically studied. It is shown that in the region of strong asymmetry the system becomes spatially fully synchronized, even in the thermodinamic…
We provide sufficient conditions for synchronization by noise, i.e. under these conditions we prove that weak random attractors for random dynamical systems consist of single random points. In the case of SDE with additive noise, these…
The conditions for synchronization in unidirectionally coupled chaotic oscillators are revisited. We demonstrate with typical examples that the conditional Lyapunov exponents (CLEs) play an important role in distinguishing between…
Determining conditions on the coupling strength for the synchronization in networks of interconnected oscillators is a challenging problem in nonlinear dynamics. While sophisticated mathematical methods have been used to derive conditions,…
This paper deals with asymptotic stability of a class of dynamical systems in terms of smooth Lyapunov pairs. We point out that well known converse Lyapunov results for differential inclusions cannot be applied to this class of dynamical…
Consider the planar linear switched system $\dot x(t)=u(t)Ax(t)+(1-u(t))Bx(t),$ where $A$ and $B$ are two $2\times2$ real matrices, $x \in \R^2$, and $u(.):[0,\infty[\to\{0,1\}$ is a measurable function. In this paper we consider the…
This paper presents new sufficient conditions for convergence and asymptotic or exponential stability of a stochastic discrete-time system, under which the constructed Lyapunov function always decreases in expectation along the system's…
This paper gives sufficient conditions for having complete synchronization of oscillators in connected undirected networks. The considered oscillators are not necessarily identical and the synchronization terms can be nonlinear. An…
Spatially extended dynamical systems, namely coupled map lattices, driven by additive spatio-temporal noise are shown to exhibit stochastic synchronization. In analogy with low-dymensional systems, synchronization can be achieved only if…
Fixed-time stable dynamical systems are capable of achieving exact convergence to an equilibrium point within a fixed time that is independent of the initial conditions of the system. This property makes them highly appealing for designing…
Stability of synchronization in unidirectionally coupled time-delay systems is studied using the Krasovskii-Lyapunov theory. We have shown that the same general stability condition is valid for different cases, even for the general…
A condition for the synchronizability of a pair of PDE systems, coupled through a finite set of variables, is commonly the existence of internal synchronization or internal coherence in each system separately. The condition was previously…
We characterize synchronization phenomenon in discrete-time, discrete-state random dynamical systems, with random and probabilistic Boolean networks as particular examples. In terms of multiplicative ergodic properties of the induced linear…
This paper presents a framework for the study of convergence when the nodes' dynamics may be both piecewise smooth and/or nonidentical across the network. Specifically, we derive sufficient conditions for global convergence of all node…
A sufficient condition for the stability of a system resulting from the interconnection of dynamical systems is given by the small gain theorem. Roughly speaking, to apply this theorem, it is required that the gains composition is…
We obtain sufficient conditions for the stability of the synchronized solutions for a class of coupled dynamical systems. This is accomplished by finding an analytical expression for the transverse Liapunov exponent through spectral…
We address stability of a class of Markovian discrete-time stochastic hybrid systems. This class of systems is characterized by the state-space of the system being partitioned into a safe or target set and its exterior, and the dynamics of…