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...

In this paper three algorithms of control of chaos (destohastization, control with proportional feedback and control with time-delayed feedback) in the process of continuous mass crystallization of dibasic lead phosphite are offered. The first method involves a corrective action in compliance with the required values of the dynamic variables and, therefore, involves a feedback as a necessary co...

In this paper, the new concept of non-autonomous iterated function system is introduced and also shown that non-autonomous iterated function system IFS(f_(1,∞)^0,f_(1,∞)^1) is topologically transitive for the metric space of X whenever the system has average shadowing property and its minimal points on X are dense. Moreover, such a system is topologically transitive, whenever, there is a point ...

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...

The Kaplan-Yorke conjecture suggests a simple relationship between the fractal dimension of a system and its Lyapunov spectrum. This relationship has important consequences in the broad field of nonlinear dynamics where dimension and Lyapunov exponents are frequently used descriptors of system dynamics. We develop an experimental system with controllable dimension by making use of the Kaplan-Yo...

(Preface page 4 L. -13) Yorke (1990) should be Nusse and Yorke (1990). p. 4 (L. -2) Subsections 8.3.1 – 4 p. 10 (L. -3) “could be combined with the section in Chapter VIII).” p. 17 (L. 2) {(x, f(x)} should read {(x, f(x))}. p. 24 (L. -12) should be “compact nested nonempty sets.” p. 24 (L. -4) should be “ . . . is closed and positively invariant . . . ” p. 27 (L. 3) “A non-empty set S . . . ” p...

Chaotic systems are highly susceptible to control by using small perturbations to a system constraint. Feedback methods have been applied to taming chaos in magnetoelastic and hydrodynamic systems, electric circuits, lasers, chemical reactions, and tissues of heart and brain in vitro.1 The well-known Ott-Grebogi-Yorke (OGY) algorithm2 and its variations are based on the notion that for controll...

In this article, we further consider the above system. In particular, we give a sufficient condition under which the above system is Kato chaotic for $eta=0$ and a necessary condition for the above system to be Kato chaotic for $eta=0$. Moreover, it is deduced that for $eta=0$, if $Theta$ is P-chaotic then so is this system, where a continuous map $Theta$ from a compact metric space $Z$ to itse...