Related papers: Finding the effective dynamics to make rare events…
We investigate the dynamics of an array of logistic maps coupled with random delay times. We report that for adequate coupling strength the array is able to synchronize, in spite of the random delays. Specifically, we find that the…
We consider the singularly perturbed limit of periodically excited two-dimensional FitzHugh-Nagumo systems. We show that the dynamics of such systems are essentially governed by an one-dimensional map and present a numerical scheme to…
The quantum dynamics of initial coherent states is studied in the Dicke model and correlated with the dynamics, regular or chaotic, of their classical limit. Analytical expressions for the survival probability, i.e. the probability of…
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…
Here we define natural chaotic systems, like the earths weather and climate system, as chaotic systems which are open to the world so have constantly changing boundary conditions, and measurements of their states are subject to errors. In…
Abrupt and rapid high-amplitude changes in a dynamical system's states known as extreme event appear in many processes occurring in nature, such as drastic climate patterns, rogue waves, or avalanches. These events often entail catastrophic…
We continue our study of chaotic mixing and transport of passive particles in a simple model of a meandering jet flow [Prants, et al, Chaos {\bf 16}, 033117 (2006)]. In the present paper we study and explain phenomenologically a connection…
The phase ordering dynamics of coupled chaotic bistable maps on lattices with defects is investigated. The statistical properties of the system are characterized by means of the average normalized size of spatial domains of equivalent spin…
The control of chaotic systems implies inducing an unpredictable system to follow a desired trajectory using the smallest "force". In low-dimensional continuous systems, one method is that of reconstructing the tangent space, so that the…
This article examines the subtle relationship between chaos and randomness, two concepts that, although they refer to seemingly unpredictable phenomenon, are based on fundamentally different principles. Chaos manifests in deterministic…
Certain deterministic non-linear systems may show chaotic behaviour. Time series derived from such systems seem stochastic when analyzed with linear techniques. However, uncovering the deterministic structure is important because it allows…
Motivated by the study of the time evolution of random dynamical systems arising in a vast variety of domains --- ranging from physics to ecology ---, we establish conditions for the occurrence of a non-trivial asymptotic behaviour for…
We present in this paper, the synchronization dynamics observed in a network of mutually coupled simple chaotic systems. The network consisting of chaotic systems arranged in a square matrix network is studied for their different types of…
We give general sufficient conditions to prove the convergence of marked point processes that keep record of the occurrence of rare events and of their impact for non-autonomous dynamical systems. We apply the results to sequential…
Dynamics in biological networks are in general robust against several perturbations. We investigate a coupled map network as a model motivated by gene regulatory networks and design systems which are robust against phenotypic perturbations…
Everything you ever wanted to know about what has come to be known as ``chaotic mixing:'' This paper describes the evolution of localised ensembles of initial conditions in 2- and 3-D time-independent potentials which admit both regular and…
A discrete-time model of reacting evolving fields, transported by a bidimensional chaotic fluid flow, is studied. Our approach is based on the use of a Lagrangian scheme where {\it fluid particles} are advected by a $2d$ symplectic map…
We study statistical properties of a family of maps acting in the space of integer valued sequences, which model dynamics of simple deterministic traffic flows. We obtain asymptotic (as time goes to infinity) properties of trajectories of…
Deterministic chaos is phenomenon from nonlinear dynamics and it belongs to greatest advances of twentieth-century science. Chaotic behavior appears apart of mathematical equations also in wide range in observable nature, so as in there…
In problems where the temporal evolution of a nonlinear system cannot be followed, a method for studying the fluctuations of spatial patterns has been developed. That method is applied to well-known problems in deterministic chaos (the…