Technical Physics, Vol. 49, No. 7, 2004, pp. 805–809. Translated from Zhurnal TekhnicheskoÏ Fiziki, Vol. 74, No. 7, 2004, pp. 1–5. Original Russian Text Copyright © 2004 by Vladimirov, Shtraukh. THEORETICAL AND MATHEMATICAL PHYSICS Entropy Control in Discrete- and Continuous-Time Dynamic Systems S. N. Vladimirov* and A. A. Shtraukh Tomsk State University, Tomsk, 634050 Russia *e-mail:
[email protected],
[email protected] Received August 14, 2003; in final form, December 22, 2003 Abstract—The dynamics of a modified logistic mapping are considered for a system with the order parameter modulated by an external signal. It is shown that the Kolmogorov–Sinay entropy changes with changing mod- ulation depth, while the harmonic signals and white noise can be used as a modulating signal. The conditions for the excitation of regular and strange nonchaotic attractors in the phase space are established. © 2004 MAIK “Nauka/Interperiodica”. INTRODUCTION modulation of the order parameter, this mapping takes At present, random oscillations have been observed the form in a great variety of objects, starting with crude x = Φ()x , mod 1, mechanical systems and ending with highly organized n + 1 n biological systems. In the theoretical and applied stud- 2π (1) Φ()x = 1 – α 1 + msin ------ n + ϕ x . ies of determinate chaos, one can distinguish a number n 0 T 0 n of priorities such as the elaboration of new scenarios for α ≥ ≤ ≤ the transition from regular to chaotic motion, methods Here, 0 1 is the order parameter; 0 m 1 is the of generating dynamic chaos, the study of the interac- order-parameter modulation depth (control parameter); ϕ tions between chaotic systems and the possible types of T and 0 are, respectively, the period and initial phase their collective behavior, unconventional dynamics and of the external force; and n = 0, 1, 2, …, N is the discrete informational processes, and entropy control in contin- time.