An approach is proposed for making a given stable continuous-time Takagi-Sugeno (TS) fuzzy-system chaotic, by first discretizing it and then using state feedback control of arbitrarily small magnitude. The feedback controller chosen among several candidates is a simple sinusoidal function of the system states, which can lead to uniformly bounded state vectors of the controlled system with posit...

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...

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...

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...

This study explores the dynamics of two monopoly models with knowledgeable players. The first model was initially introduced by Naimzada and Ricchiuti, while second one is simplified famous Puu. We employ several tools based on symbolic computations to analyze local stability bifurcations models. To best our knowledge, complete conditions are obtained for time. investigate periodic solutions th...

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...