Related papers: Synchronization of Chaotic Systems by Common Rando…
Recently, we introduced a new test for distinguishing regular from chaotic dynamics in deterministic dynamical systems and argued that the test had certain advantages over the traditional test for chaos using the maximal Lyapunov exponent.…
We investigate functions that are exact solutions to chaotic dynamical systems. A generalization of these functions can produce truly random numbers. For the first time, we present solutions to random maps. This allows us to check,…
A method of targeting engineering synchronization states in two identical and mismatch chaotic systems is explained in details. The method is proposed using linear feedback controller coupling for engineering synchronization such as mixed…
We prove the existence of Noise Induced Order in the Matsumoto-Tsuda model, where it was originally discovered in 1983 by numerical simulations. This is a model of the famous Belosouv-Zabotinsky reaction, a chaotic chemical reaction, and…
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…
For a product of i.i.d. random maps or a memoryless stochastic flow on a compact space $X$, we find conditions under which the presence of locally asymptotically stable trajectories (e.g. as given by negative Lyapunov exponents) implies…
We characterize the macroscopic attractor of infinite populations of noisy maps subjected to global and strong coupling by using an expansion in order parameters. We show that for any noise amplitude there exists a large region of strong…
Despite the prominent importance of the Lyapunov exponents for characterizing chaos, it still remains a challenge to measure them for large experimental systems, mainly because of the lack of recurrences in time series analysis. Here we…
A new approach is proposed to the integrated analysis of the time structure of synchronization of multidimensional chaotic systems. The method allows one to diagnose and quantitatively evaluate the intermittency characteristics during…
Algorithms increasingly operate within complex physical, social, and engineering systems where they are exposed to disturbances, noise, and interconnections with other dynamical systems. This article extends known convergence guarantees of…
Finding conditions that support synchronization is a fertile and active area of research with applications across multiple disciplines. Here we present and analyze a scheme for synchronizing chaotic dynamical systems by transiently…
The present paper explores the synchronization scenario of hyperchaotic time-delayed electronic oscillators coupled indirectly via a common environment. We show that depending upon the coupling parameters a hyperchaotic time-delayed system…
We investigate bifurcation phenomena between slow and fast convergences of synchronization errors arising in the proposed synchronization system consisting of two identical nonlinear dynamical systems linked by a common noisy input only.…
We focus on chaotic dynamical systems and analyze their time series with the use of autoencoders, i.e., configurations of neural networks that map identical output to input. This analysis results in the determination of the latent space…
We demonstrate the extension of unpredictable motions in coupled autonomous systems with skew product structure in the case that generalized synchronization takes place. Sufficient conditions for the existence of unpredictable motions in…
Low-dimensional chaotic systems such as the Lorenz-63 model are commonly used to benchmark system-agnostic methods for learning dynamics from data. Here we show that learning from noise-free observations in such systems can be achieved up…
We provide sufficient conditions for weak synchronization by noise for order-preserving random dynamical systems on Polish spaces. That is, under these conditions we prove the existence of a weak point attractor consisting of a single…
We present the first report on chaos synchronization between two unidirectionally linearly and nonlinearly coupled systems with multiple time-delays and using the Razumikhin-Lyapunov approach find the existence and stability conditions for…
We prove the existence of multiple noise-induced transitions in the Lasota-Mackey map, which is a class of one dimensional random dynamical system with additive noise. The result is achieved by the help of rigorous computer assisted…
Given two unidirectionally coupled nonlinear systems, we speak of generalized synchronization when the responder \textquotedblleft follows\textquotedblright\ the driver. Mathematically, this situation is implemented by a map from the driver…