A variety of methods have been developed in nonlinear science to stabilize unstable periodic orbits (UPOs) and control chaos [1], following the seminal work by Ott, Grebogi and Yorke [2], who employed a tiny control force to stabilize UPOs embedded in a chaotic attractor [3, 4]. A particularly simple and efficient scheme is time-delayed feedback as suggested by Pyragas [5], which uses the diffe...

This paper yields process of development, numerical analysis, lumped circuit modeling, and experimental verification a new hyperchaotic oscillator based on the fundamental topology two-stage amplifier. Analyzed network structure contains two generalized bipolar transistors connected with common emitter. Both are initially modeled as two-ports via full admittance matrix, considering linear backw...

Controlling chaos has been an extremely active area of research in applied dynamical systems, following the introduction of the Ott, Grebogi, Yorke (OGY) technique in 1990 [Ott et al., 1990], but most of this research based on parametric feedback control uses local techniques. Associated with a dynamical system which pushes forward initial conditions in time, transfer operators, including the F...

It has been well-known that tight relationship exists between chaos and cryptography [Brown & Chua, 1996]. Many fundamental characteristics of chaos, such as ergodicity, mixing property and sensitivity to initial conditions/control parameters [Hao, 1993], can be connected with some cryptographic properties of good ciphers, such as confusion/diffusion, balance and avalanche property [Schneier, 1...

The attractor dimension at the transition to complete synchronization in a network of chaotic units with time-delayed couplings is investigated. In particular, we determine the Kaplan-Yorke dimension from the spectrum of Lyapunov exponents for iterated maps and for two coupled semiconductor lasers. We argue that the Kaplan-Yorke dimension must be discontinuous at the transition and compare it t...

A number of new relations between the Kaplan Yorke dimension, phase space contraction, transport coefficients and the maximal Lyapunov exponents are given for dissipative thermostatted systems, subject to a small but non-zero external field in a nonequilibrium stationary state. A condition for the extensivity of phase space dimension reduction is given. A new expression for the linear transport...

Mr. Tien-Yien Li, of Hunan ancestry, was born in June of 1945 in Sha County, Fujian Province of China. His father, Ding-Xun Li, studied overseas at the medical school of Tokyo Imperial University and received a medical doctorate degree. In 1934, he returned to China and became a faculty member of Hunan Xiang-ya Medical School. In 1939, he served as president of Fujian Provincial Medical College...

Chaotic attractors contain unstable periodic orbits of any desired period (this is shown in chapter 22 for Axiom A attractors). Furthermore, for an ergodic attractor we know that any trajectory will eventually come arbitrarily close to any of these orbits. This offers the opportunity for controlling chaos: when the chaotic orbit approaches the unstable periodic orbit of interest it can be attra...

Since the beginning of the 90s a new direction appeared in the theory of dynamical systems, which was called “Controlling chaos”. The subject of this field is how to transform chaotic behavior to a regular one or to a more simple chaotic one by means of special small influence on the dynamical system. Pioneer works of this new direction were papers by Hubler and Lucher [1989], Jackson [1990] an...