Hamburg 2001 – scientific programme

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DY: Dynamik und Statistische Physik

DY 13: Statistische Physik (Allgemein) II

DY 13.2: Talk

Monday, March 26, 2001, 10:45–11:00, S 7

Elementary chaotic flows — •Stefan J. Linz¹ and J. C. Sprott² — ¹Theoretische Physik I, Universität Augsburg, 86135 Augsburg — ²Department of Physics, University of Wisconsin, Madison WI 53706, USA

Searching for elementary chaotic flows and a classification scheme based on their functional complexity, autonomous scalar third-order differential equations (jerky dynamics) seem to be an appropriate point of departure. By combining extensive numerical searches for chaotic behavior in such systems [1,2] and analytical no-chaos criteria [1,3], we are able [4] to (i) identify minimal chaotic flows with quasi-linear and other types of nonlinearities, (ii) obtain insights in the interplay between the functional form of the entering nonlinearity and the potential chaotic behavior of such models, and (iii) generalize a previously suggested classification scheme for chaotic jerky dynamics with quadratic nonlinearities [5] to arbitrary nonlinearities.

[1] Linz, Sprott, Phys. Lett. A 259, 240 (1999);

[2] Sprott, Phys. Lett. A 266, 19 (2000);

[3] Linz, Phys. Lett. A 275, 204 (2000);

[4] Linz, Sprott, in preparation;

[5] Eichhorn, Linz, Hanggi, Phys. Rev. E 58, 7151 (1998)