Related papers: Chaos suppression in the parametrically driven Lor…

We show two examples of noise--induced synchronization. We study a 1-d map and the Lorenz systems, both in the chaotic region. For each system we give numerical evidence that the addition of a (common) random noise, of large enough…

In order to analyze the effect of chaos or order on the rate of decoherence in a subsystem we aim to distinguish effects of the two types of dynamics from those depending on the choice of the wave packet. To isolate the former we introduce…

We consider a $N$-particle system interacting through the Newtonian potential with a polynomial cut-off in the presence of noise in velocity. We rigorously prove the propagation of chaos for this interacting stochastic particle system.…

Recent studies have extensively explored chaotic dynamics in quantum optical systems through the mean-field approximation, which corresponds to an ideal, fluctuation-free scenario. However, the inherent sensitivity of chaos to initial…

We consider a new fractional order chaotic system displaying an interesting behavior. A necessary condition for the system to remain chaotic is derived. It is found that chaos exists in the system with order less than three. Using the…

In order to analyze the effect of chaos or order on the rate of decoherence in a subsystem, we aim to distinguish effects of the two types of dynamics by choosing initial states as random product states from two factor spaces representing…

Simple dynamical systems -- with a small number of degrees of freedom -- can behave in a complex manner due to the presence of chaos. Such systems are most often (idealized) limiting cases of more realistic situations. Isolating a small…

A method to reduce or enhance chaos in Hamiltonian flows with two degrees of freedom is discussed. This method is based on finding a suitable perturbation of the system such that the stability of a set of periodic orbits changes (local…

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…

The efficient detection of chaotic behavior in orbits of a complex dynamical system is an active domain of research. Several indicators have been proposed in the past, and new ones have recently been developed in view of improving the…

We propose a mechanism which produces periodic variations of the degree of predictability in dynamical systems. It is shown that even in the absence of noise when the control parameter changes periodically in time, below and above the…

A three-component dynamic system with influence of pumping and nonlinear dissipation describing a quantum cavity electrodynamic device is studied. Different dynamical regimes are investigated in terms of divergent trajectories approaches…

We present numerical and analytical studies of a quantum computer proposed by the Yamamoto group in Phys. Rev. Lett. 89, 017901 (2002). The stable and quantum chaos regimes in the quantum computer hardware are identified as a function of…

It is shown that a relevant control of Hamiltonian chaos is possible through suitable small perturbations whose form can be explicitly computed. In particular, it is possible to control (reduce) the chaotic diffusion in the phase space of a…

We propose an uncertainty principle for chaos, focusing on two key characteristics: alpha unpredictability and Lorenz sensitivity. This principle outlines a limitation on the relationship between two infinite sequences that underpin these…

We consider time-periodically perturbed 1D Hamiltonian systems possessing one or more separatrices. If the perturbation is weak, then the separatrix chaos is most developed when the perturbation frequency lies in the logarithmically small…

The R\"ossler System is one of the best known chaotic dynamical systems, exhibiting a plethora of complex phenomena - and yet, only a few studies tackled its complexity analytically. In this paper we find sufficient conditions for the…

This paper provides a unified method for analyzing chaos synchronization of the generalized Lorenz systems. The considered synchronization scheme consists of identical master and slave generalized Lorenz systems coupled by linear state…

We show that the fluctuations of the periodic orbits of deterministically chaotic systems can be captured by supersymmetry, in the sense that they are repackaged in the contribution of the absolute value of the determinant of the noise…

We introduce a novel type of random perturbation for the classical Lorenz flow in order to better model phenomena slowly varying in time such as anthropogenic forcing in climatology and prove stochastic stability for the unperturbed flow.…