Related papers: The Origin of Non-chaotic Behavior in Identically …
Pairs of numerically computed trajectories of a chaotic system may coalesce because of finite arithmetic precision. We analyse an example of this phenomenon, showing that it occurs surprisingly frequently. We argue that our model belongs to…
Noise-induced failures in the stabilization of an unstable orbit in the one-dimensional logistic map are considered as large fluctuations from a stable state. The properties of the large fluctuations are examined by determination and…
In this paper we present an analytical study on the synchronization dynamics observed in unidirectionally-coupled quasiperiodically-forced systems that exhibit Strange Non-chaotic Attractors (SNA) in their dynamics. The SNA dynamics…
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…
Empirical results show that PSO performance may be different if using either chaotic or random sequences to drive the algorithm's search dynamics. We analyze the phenomenon by evaluating the performance based on a benchmark of test…
This article provides a self-contained comprehensive review of the phenomenon of synchronization in dynamical systems, with a particular focus on chaotic systems in both continuous-time and discrete-time contexts. Synchronization, initially…
Coherence resonance can be explained using differential entropy and mutual information. This theory explores the role of external noise in stabilising chaotic circuits such as the uni-junction transistor relaxation oscillator.The phenomenon…
A gas of interacting particles is a paradigmatic example of chaotic systems. It is shown here that even if all but one particle are fixed in generic positions, the excited states of the moving particle are chaotic. They are characterized by…
Problems with artificial neural networks originate from their deterministic nature and inevitable prior learnings, resulting in inadequate adaptability against unpredictable, abrupt environmental change. Here we show that a stochastically…
In nonlinear systems analysis, minor fractions of higher-order dynamics are often neglected for simplicity. Here, we show that machine epsilon levels of parasitic higher-order dynamics due to computer roundoff alone can cause divergence of…
The effect of impurities in a two-dimensional lattice of coupled nonlinear chaotic oscillators and their ability to control the dynamical behavior of the system are studied. We show that a single impurity can produce synchronized…
Many real-world complex systems rely on cluster synchronization to function properly. A cluster of nodes exhibits synchronous behavior while others behave erratically. Predicting the emergence of these clusters and understanding the…
We study the noise effects in a driven system of globally coupled oscillators, with particular attention to the interplay between driving and noise. The self-consistency equation for the order parameter, which measures the collective…
The paper considers a stabilizing stochastic control which can be applied to a variety of unstable and even chaotic maps. Compared to previous methods introducing control by noise, we relax assumptions on the class of maps, as well as…
Based on the principle of chaotification for continuous-time autonomous systems, which relies on two basic properties of chaos, i.e., globally bounded with necessary positive-zero-negative Lyapunov exponents, this paper derives a feasible…
We study data-driven stabilization of continuous-time systems in autoregressive form when only noisy input-output data are available. First, we provide an operator-based characterization of the set of systems consistent with the data. Next,…
Dynamical Systems theory generally deals with fixed point iterations of continuous functions. Computation by Turing machine although is a fixed point iteration but is not continuous. This specific category of fixed point iterations can only…
We describe adaptive control algorithms whereby a chaotic dynamical system can be steered to a target state with desired characteristics. A specific implementation considered has the objective of directing the system to a state which is…
Colloidal bodies of irregular shape rotate as they descend under gravity in solution. This rotational response provides a means of bringing a dispersion of identical bodies into a synchronized rotation with the same orientation using…
As a result of resonance overlap, planetary systems can exhibit chaotic motion. Planetary chaos has been studied extensively in the Hamiltonian framework, however, the presence of chaotic motion in systems where dissipative effects are…