Analysis of nonlinear autonomous systems has been a popular field of study in recent decades. As an interesting nonlinear behavior, chaotic dynamics has been intensively investigated since Lorenz discovered the first physical evidence of chaos in his famous equations. Although many chaotic systems have been ever reported in the literature, a systematic and qualitative approach for chaos generat...

Ensemble averages of the sensitivity to initial conditions xi(t) and the entropy production per unit of time of a new family of one-dimensional dissipative maps, x(t+1)=1-ae(-1/|x(t)|(z))(z>0), and of the known logisticlike maps, x(t+1)=1-a|x(t)|(z)(z>1), are numerically studied, both for strong (Lyapunov exponent lambda(1)>0) and weak (chaos threshold, i.e., lambda(1)=0) chaotic cases. In all ...

We analyze the Eckhaus instability of plane waves in the one-dimensional complex Ginzburg-Landau equation (CGLE) and describe the nonlinear effects arising in the Eckhaus unstable regime. Modulated amplitude waves (MAWs) are quasiperiodic solutions of the CGLE that emerge near the Eckhaus instability of plane waves and cease to exist due to saddle-node bifurcations (SN). These MAWs can be chara...

It is demonstrated experimentally and theoretically that through the use of an active (feedback) controller one can dramatically modify the nature of the flow in a toroidal thermal convection loop heated from below and cooled from above. In particular, we show how a simple control strategy can be used to suppress (laminarize) the naturally occurring chaotic motion or induce chaos in otherwise t...

OBJECTIVE To test whether family chaos influences adolescents' inflammatory profiles and whether adolescents from low socioeconomic status (SES) environments are at higher risk for experiencing adverse inflammatory profiles from living in chaotic family environments. METHODS A total of 244 families with an adolescent aged 13 to 16 years participated. Parents completed measures of family SES a...

The studies of the phenomenon of chaos synchronization are usually based upon the analysis of the existence of transversely stable invariant manifold that contains an invariant set of trajectories corresponding to synchronous motions. In this paper we develop a new approach that relies on the notions of topological synchronization and the dimension for Poincaré recurrences. We show that the dim...

(1959) Chirikov criterion (1969) Classical map: ¯ p = p + K sin x ¯ x = x + ¯ p (1979) Quantum map (kicked rotator): ¯ ψ = e −î p 2 /2 e −iK / cosˆx ψ (1959-2008) Hamiltonian classical / quantum chaos : H (ˆ p , ˆ x) = ˆ p 2 / 2 + K cosˆx m δ (t − m) [ ˆ p , ˆ x ] = −i (2001) Quantum computations (2008) Ongoing experiments with cold atoms and Bose-Einstein condensates

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 that logistis, Baker’s, Tinckerbel’s in classical or quantum systems. In this paper, we give a new treatment of quantum chaos by defining the entropic chaos ...

The aim of this paper is to investigate the existence of Parrondo’s paradox for the logistic family fa(x) = ax(1−x), x ∈ [0, 1], when the parameter value a ranges over the interval [1, 4]. We find that a paradox of type “order + order = chaos” arises for both physically observable and topological chaos, while a “chaos + chaos = order” paradox can be only detected for the case of physically obse...