We present an elementary derivation of chaos control with simple limiters using the logistic map and the Henon map as examples. This derivation provides conditions for optimal stabilization of unstable periodic orbits of a chaotic attractor.

Noise-induced escape from a non-hyperbolic attractor, and from a quasihyperbolic attractor with nonfractal boundaries, is investigated by means of analogue experiments and numerical simulations. It is found that there exists a most probable (optimal) escape trajectory, the prehistory of the escape being de ned by the structure of the chaotic attractor. The corresponding optimal uctuational forc...

Exceptional point in non-Hermitian system possesses fascinating properties. We present an exactly solvable attractor dynamics for the first time from a two-level dependent Hamiltonian. It allows way to evolve coalescence state pure or mixed initial through varying imaginary parameter along specific diabatic passage. Contrast chaotic that is ultrasensitive condition, designed insensitive conditi...

A chaotic system under periodic forcing can develop a periodically visited strange attractor. We discuss simple models in which the phenomenon, quite easy to see in numerical simulations, can be completely studied analytically.

A method for multiple access using the structure of the unstable periodic orbits of chaotic attractor is proposed. Possible principles of the control and selection of unstable cycle-codes are presented.

James Yorke won the 2003 Japan Prize for his work in the field of chaos theory. This book was compiled by four of his best-known collaborators in honor of his 60th birthday and contains papers by various authors on chaos and chaotic attractors. The papers are organized around the topics of “natural” invariant measure and fractal dimension of the associated chaotic attractors. A few of the paper...

The effects of intrinsic spontaneous-emission noise on the nonlinear dynamics of an optically injected semiconductor laser is quantitatively studied through a single-mode model. It is found that for periodic motions, the effect of this noise source is to kick phase points off the underlying deterministic limit cycle. When the noise is not too strong so that phase points can stay near the limit ...

In this paper, we discuss the reconstruction of chaotic dynamics by using a normalized Gaussian network (NGnet), which is a network of local linear regression units. The NGnet is trained by an on-line EM algorithm in order to learn the vector field of the chaotic dynamics. We investigate the robustness of our approach to two kinds of noise processes: system noise and observation noise. System n...

In many situations, the existence of several equilibrium points in a dynamical system makes its dynamics more complex and allows some special structures. Examples include the well-known multiscroll attractors ([Wang, 2009; Qi et al., 2008; Liu & Chen, 2004; Li, 2008; Wang et al., 2009; Lü et al., 2008; Yu et al., 2006; Yu et al., 2008, 2010a; Wang & Chen, 2012] and references therein) such as c...