Related papers: How does noise affect the structure of a chaotic a…
We propose an entropy measure for the analysis of chaotic attractors through recurrence networks which are un-weighted and un-directed complex networks constructed from time series of dynamical systems using specific criteria. We show that…
Recurrence networks and the associated statistical measures have become important tools in the analysis of time series data. In this work, we test how effective the recurrence network measures are in analyzing real world data involving two…
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…
Anatomical studies demonstrate that brain reformats input information to generate reliable responses for performing computations. However, it remains unclear how neural circuits encode complex spatio-temporal patterns. We show that neural…
This paper summarises an investigation of the effects of low amplitude noise and periodic driving on phase space transport in 3-D Hamiltonian systems, a problem directly applicable to systems like galaxies, where such perturbations reflect…
Attractors of dynamical systems may be networks in phase space that can be heteroclinic (where there are dynamical connections between simple invariant sets) or excitable (where a perturbation threshold needs to be crossed to a dynamical…
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 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…
We study the effects of additive noise on the lifetimes of chaotic repellors. Using first order perturbation theory we argue that noise will increase the lifetime if the escape holes lie in regions where the unperturbed density is higher…
In principle, the state space of a chaotic attractor can be partially or wholly reconstructed from interspike intervals recorded from experiment. Under certain conditions, the quality of a partial reconstruction, as measured by the spike…
Recurrence networks are powerful tools used effectively in the nonlinear analysis of time series data. The analysis in this context is done mostly with unweighted and undirected complex networks constructed with specific criteria from the…
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…
Noise modifies the behavior of chaotic systems in both quantitative and qualitative ways. To study these modifications, the present work compares the topological structure of the deterministic Lorenz (1963) attractor with its stochastically…
First passage time experiments were used to explore the effects of low amplitude noise as a source of accelerated phase space diffusion in two-dimensional Hamiltonian systems, and these effects were then compared with the effects of…
The dynamics of a weakly dissipative Hamiltonian system submitted to stochastic perturbations has been investigated by means of asymptotic methods. The probability of noise-induced separatrix crossing, which drastically changes the fate of…
The effect of additive white noise on a model for bursting behavior in large aspect-ratio binary fluid convection is considered. Such bursts are present in systems with nearly square symmetry and are the result of heteroclinic cycles…
A new type of noised-induced phase transitions that should occur in systems of elements with motivated behavior is considered. By way of an example, a simple oscillatory system {x,v} with additive white noise is analyzed numerically. A…
Recurrence analysis is a well settled method allowing to discern chaos from order, and determinism from noise. We apply this tool to study time series representing geodesic and inspiraling motion of a test particle in a deformed Kerr…
As a phenomenon in dynamical systems allowing autonomous switching between stable behaviors, chaotic itinerancy has gained interest in neurorobotics research. In this study, we draw a connection between this phenomenon and the predictive…
We consider a white noise perturbation of dynamics in the neighborhood of a heteroclinic network. We show that under the logarithmic time rescaling the diffusion converges in distributon in a special topology to a piecewise constant process…