Related papers: Noise-driven Topological Changes in Chaotic Dynami…
Random attractors are the time-evolving pullback attractors of stochastically perturbed, deterministically chaotic dynamical systems. These attractors have a structure that changes in time, and that has been characterized recently using…
Effect of noise in inducing order on various chaotically evolving systems is reviewed, with special emphasis on systems consisting of coupled chaotic elements. In many situations it is observed that the uncoupled elements when driven by…
We investigate the effects of a time-correlated noise on an extended chaotic system. The chosen model is the Lorenz'96, a kind of toy model used for climate studies. The system is subjected to both temporal and spatiotemporal perturbations.…
We investigate the effects of a time-correlated noise on an extended chaotic system. The chosen model is the Lorenz'96, a kind of "toy" model used for climate studies. Through the analysis of the system's time evolution and its time and…
Chaotic systems which are due to nonlinearity have attracted a great concern in the current world and chaotic models. Systems for a wide range of operation conditions have their application in almost all branches of engineering and science.…
We study the constructive role of noises in a Lorenz system with functional delay. The effect of delay can change the dynamics of the system to a chaotic one from its steady state. Induced synchronization with white and colored (red and…
We undertake a preliminary numerical investigation to understand how the addition of white and colored noise to a time series affects the topology and structure of the underlying chaotic attractor. We use the methods and measures of…
We evoke the idea of representation of the chaotic attractor by the set of unstable periodic orbits and disclose a novel noise-induced ordering phenomenon. For long unstable periodic orbits forming the strange attractor the weights (or…
Biological systems operate under persistent noise, which can alter system states and induce transitions between attractors. Here, we study the attractor dynamics of Boolean networks focusing on the transitions between attractors induced by…
Chaotic bursting behaviors have been observed by many authors in neural dynamics mainly in the transition between different kinds of bursting behavior. As a well-known three-dimensional ODEs model with various bursting solutions, the…
We develop the characterization of the dynamics at the noise-perturbed edge of chaos in logistic maps in terms of the quantities normally used to describe glassy properties in structural glass formers. Following the recognition [Phys. Lett.…
We study the effect that the injection of a common source of noise has on the trajectories of chaotic systems, addressing some contradictory results present in the literature. We present particular examples of 1-d maps and the Lorenz…
Poincar\'e recognized that phase portraits are mainly structured around fixed points. Nevertheless, the knowledge of fixed points and their properties is not sufficient to determine the whole structure of chaotic attractors. In order to…
Nonlinear dynamical systems subjected to a combination of noise and time-varying forcing can exhibit sudden changes, critical transitions or tipping points where large or rapid dynamic effects arise from changes in a parameter that are…
The theoretical and numerical understanding of the key concept of topological entropy is an important problem in dynamical systems. Most studies have been carried out on maps (discrete-time systems). We analyse a scenario of global changes…
We study the homology of simplicial complexes built via deterministic rules from a random set of vertices. In particular, we show that, depending on the randomness that generates the vertices, the homology of these complexes can either…
Time evolution of diluted neural networks with a nonmonotonic transfer function is analitically described by flow equations for macroscopic variables. The macroscopic dynamics shows a rich variety of behaviours: fixed-point, periodicity and…
Motivated by a stochastic differential equation describing the dynamics of interfaces, we study the bifurcation behavior of a more general class of such equations. These equations are characterized by a 2-dimensional phase space (describing…
A two dimensional flow model is introduced with deterministic behavior consisting of bursts which become successively larger, with longer interburst time intervals between them. The system is symmetric in one variable x and there are bursts…
Strange nonchaotic attractors (SNAs) in noise driven systems are investigated. Before the transition to chaos, due to the effect of noise, a typical trajectory will wander between the periodic attractor and its nearby chaotic saddle in an…