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...

This paper is concerned with invariance (F1,F2)-scrambled sets under iterations. The main results are an extension of the compound invariance of Li–Yorke chaos and distributional chaos. New definitions of (F1,F2)-scrambled sets in non-autonomous discrete systems are given. For a positive integer k, the properties P(k) and Q(k) of Furstenberg families are introduced. It is shown that, for any po...

We study the existence of snap-back repellers, hence the existence of transversal homoclinic orbits in a discrete-time neural network. Chaotic behaviors for the network system in the sense of Li and Yorke or Marotto can then be concluded. The result is established by analyzing the structures of the system and allocating suitable parameters in constructing the fixed points and their pre-images f...

Some simple equations representing the dynamics of a single population over time are known to be capable of generating extremely complicated behavior. This complicated behavior has been termed chaotic (Li and Yorke, 1975; May, 1974, 1975; May and Oster, 1976; Guckenheimer et al., 1976). The practical consequence of chaotic behavior is a certain inability to describe particular population trajec...

Wolfram divided the 256 elementary cellular automata rules informally into four classes using dynamical concepts like periodicity, stability, and chaos. Rule 14, which is Bernoulli στ -shift rule and is a member of Wolfram’s class II, is said to be simple as periodic before. Therefore, it is worthwhile studying dynamical behaviors of rule 14, whether it possesses chaotic attractors or not. In t...

In this work, we analyzed the impact of interventions on populations which exhibit unimodal dynamics. The six landmarks that characterize the “shape” of the unimodal reproduction curve   f x of the difference equation,   1 n n X f X   , are defined and used in order to examine and determine the behavior of dynamics of populations. By using the Li-Yorke criterion for determination of chaos...

Proteinase Inhibitors: Medical and Biological Aspects (Katunuma, N., ed.), pp. 97-109, Springer-Verlag Co., New York Roisen, F. J., Wilson, F. J., Yorke, G., Inczedy-Marcsek, M. & Hirabayashi, T. (19836) J. Muscle Res. Cell. Motility 4, 163-175 Schwartz, W. N. & Bird, J . W. C. (1977) Biochem. J . 167,811 -820 St. John, A. C., McElligott, M. A., Lee, J. A., Keaton, K. S., Yorke, G . , Roisen, F...