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The influence of noise on the generalized synchronization regime in the chaotic systems with dissipative coupling is considered. If attractors of the drive and response systems have an infinitely large basin of attraction, generalized…
Control over the quantum dynamics of chaotic kicked rotor systems is demonstrated. Specifically, control over a number of quantum coherent phenomena is achieved by a simple modification of the kicking field. These include the enhancement of…
The paper is focused on the discussion of the phenomenon of transitional chaos in dynamic autonomous and non-autonomous systems. This phenomenon involves the disappearance of chaotic oscillations in specific time periods and the system…
We introduce the notion of domain-structured chaos and apply it to establish a connection between stochastic dynamics and deterministic chaos.
We characterize synchronization phenomenon in discrete-time, discrete-state random dynamical systems, with random and probabilistic Boolean networks as particular examples. In terms of multiplicative ergodic properties of the induced linear…
As a main step in the numerical solution of control problems in continuous time, the controlled process is approximated by sequences of controlled Markov chains, thus discretising time and space. A new feature in this context is to allow…
A measure describing the chaos of a dynamics was introduced by two complexities in information dynamics, and it is called the chaos degree. In particular, the entropic chaos degree has been used to characterized several dynamical maps such…
In this paper, we introduce the notion of distributional chaos and the measure of chaos for random dynamical systems generated by two interval maps. We give some sufficient conditions for a zero measure of chaos and examples of chaotic…
In classical statistical mechanics there is a clear correlation between relaxation to equilibrium and chaos. In contrast, for isolated quantum systems this relation is -- to say the least -- fuzzy. In this work we try to unveil the…
We present a rigorous reassessment of chaotic behavior in two-dimensional autonomous systems with singular or nonsmooth dynamics. For the Cummings-Dixon-Kaus (CDK) model, we show that blow-up regularization restores smoothness and renders…
Chaotic cryptography is based on the properties of chaos as source of entropy. Many different schemes have been proposed to take advantage of those properties and to design new strategies to encrypt information. However, the right and…
Symbolic dynamics has proven to be an invaluable tool in analyzing the mechanisms that lead to unpredictability and random behavior in nonlinear dynamical systems. Surprisingly, a discrete partition of continuous state space can produce a…
We propose a theory of deterministic chaos for discrete systems, based on their representations in binary state spaces $ \Omega $, homeomorphic to the space of symbolic dynamics. This formalism is applied to neural networks and cellular…
We revisit the problem of switching off unwanted phase evolution and decoherence in a single two-state quantum system in the light of recent results on random dynamical decoupling methods [L. Viola and E. Knill, Phys. Rev. Lett. {\bf 94},…
We explore the behaviour of an ensemble of chaotic oscillators coupled only to an external chaotic system, whose intrinsic dynamics may be similar or dissimilar to the group. Counter-intuitively, we find that a dissimilar external system…
Characterizing the emergence of chaotic dynamics of complex networks is an essential task in nonlinear science with potential important applications in many fields such as neural control engineering, microgrid technologies, and ecological…
A deterministic coalescing dynamics with constant rate for a particle system in a finite volume with a fixed initial number of particles is considered. It is shown that, in the thermodynamic limit, with the constraint of fixed density, the…
We investigate the effect of repeated measurement for quantum dynamics of the suppressed systems which classical counterparts exhibit chaos. The essential feature of such systems is the quantum localization phenomena strongly limiting…
Stochastic dynamical systems are fundamental in state estimation, system identification and control. System models are often provided in continuous time, while a major part of the applied theory is developed for discrete-time systems.…
The appearance of chaotic quantum dynamics significantly depends on the symmetry properties of the system, and in cold atomic systems many of these can be experimentally controlled. In this work, we systematically study the emergence of…