Related papers: Random attractors on countable state spaces
We extend the Lyapunov function technique, a fundamental tool for investigating asymptotic stability and existence of attractors for ordinary differential equations, by introducing the notion of a {\it strong Lyapunov function} for an…
We numerically study a directed small-world network consisting of attractively coupled, identical phase oscillators. While complete synchronization is always stable, it is not always reachable from random initial conditions. Depending on…
We study synchronization for linearly coupled temporal networks of heterogeneous time-dependent nonlinear agents via the convergence of attracting trajectories of each node. The results are obtained by constructing and studying the…
Reflecting boundary conditions cause two one-dimensional random walks to synchronize if a common direction is chosen in each step. The mean synchronization time and its standard deviation are calculated analytically. Both quantities are…
A major challenge in neuroscience is posed by the need for relating the emerging dynamical features of brain activity with the underlying modular structure of neural connections, hierarchically organized throughout several scales. The…
It is well-known that random attractors of a random dynamical system are generally not unique. We show that for general pullback attractors and weak attractors, there is always a minimal (in the sense of smallest) random attractor which…
In many dynamical systems in nature, the law of the dynamics changes along with the temporal evolution of the system. These changes are often associated with the occurrence of certain events. The timing of occurrence of these events…
We observe the occurrence of a strange nonchaotic attractor in a periodically driven two-dimensional map, formerly proposed as a neuron model and a sequence generator. We characterize this attractor through the study of the Lyapunov…
Many seemingly disparate Markov chains are unified when viewed as random walks on the set of chambers of a hyperplane arrangement. These include the Tsetlin library of theoretical computer science and various shuffling schemes. If only…
We prove the existence of limiting distributions for a large class of Markov chains on a general state space in a random environment. We assume suitable versions of the standard drift and minorization conditions. In particular, the system…
We study a model of a polling system, that is, a collection of $d$ queues with a single server that switches from queue to queue. The service time distribution and arrival rates change randomly every time a queue is emptied. This model is…
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…
A theory on bi-spatial random attractors developed recently by Li \emph{et al.} is extended to study stochastic Fitzhugh-Nagumo system driven by a non-autonomous term as well as a general multiplicative noise. By using the so-called notions…
We study pullback attractors of non-autonomous non-compact dynamical systems generated by differential equations with non-autonomous deterministic as well as stochastic forcing terms. We first introduce the concepts of pullback attractors…
Generalized synchronization between coupled dynamical systems is a phenomenon of relevance in applications that range from secure communications to physiological modelling. Here we test the capabilities of reservoir computing and, in…
The successive discrete structures generated by a sequential algorithm from random input constitute a Markov chain that may exhibit long term dependence on its first few input values. Using examples from random graph theory and search…
An aperiodic and irreducible Markov chain on a finite state space converges to its stationary distribution. When convergence to equilibrium is measured by total variation distance, there exists an optimal coupling and a maximal coupling…
We discuss the possibility of simultaneous and sequential synchronisation in vertical and horizontal arrays of unidirectionally coupled discrete systems. This is realized for the specific case of two dimensional Gumowski-Mira maps. The…
By introducing extrinsic noise as well as intrinsic uncertainty into a network with stochastic events, this paper studies the dynamics of the resulting Markov random network and characterizes a novel phenomenon of intermittent…
The mechanism of synchronization in the random Zaslavsky map is investigated. From the error dynamics of two particles, the structure of phase space was analyzed, and a transcritical bifurcation between a saddle and a stable fixed point was…