Synthesis of chaotic systems. (English) Zbl 0832.93028

The authors propose an approach to construct a chaotic system by the synthesis of a linear dissipative single-input single-output system and a nonlinear static output feedback. An example constructed in this way is illustrated by computation.


93C15 Control/observation systems governed by ordinary differential equations
93B50 Synthesis problems
34C28 Complex behavior and chaotic systems of ordinary differential equations
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
Full Text: Link


[1] D. V. Anosov, V. I. Arnold (eds.): Dynamical Systems I. Springer, Berlin 1988. · Zbl 0658.00008
[2] V. I. Arnold: Ordinary Differential Equations. Nauka, Moscow 1971.
[3] L. O. Chua (ed.): Chaotic Systems. Spec. Iss. of Proc. IEEE 75 (1987), 8.
[4] L. O. Chua: The genesis of Chua’s circuit. AEÜ 46 (1992), 250-257.
[5] S. Čelikovský, A. Vaněček: Bilinear systems and chaos. Kybernetika 30 (1994), 404-424. · Zbl 0823.93026
[6] A. Garfinkel: The virtues of chaos. Behavioral Brain Sci. 10 (1987), 178-179.
[7] R. Genesio, A. Tesi: Chaos prediction in nonlinear feedback systems. Proc. IEE D-138 (1991), 313-320. · Zbl 0754.93024
[8] A. J. Goldberger: Nonlinear dynamics, fractals, cardiac physiology and sudden death. Temporal Disorder in Human Oscillatory Systems, Springer-Verlag, Berlin 1987, pp. 118-125.
[9] A. V. Holden (ed.): Chaos. Princeton University Press, Princeton 1986. · Zbl 0743.58005
[10] T. Kailath: Linear Systems. Prentice Hall, Englewood Cliffs 1980. · Zbl 0454.93001
[11] T. Matsumoto L. O. Chua, M. Komuro: The double scroll. IEEE Trans. CAS-32 (1985), 798-818. · Zbl 0578.94023
[12] R. Seydel: From Equilibrium to Chaos. Elsevier, New York 1988. · Zbl 0652.34059
[13] A. Vaněček: Strongly nonlinear and other control systems. Problems Control Inform. Theory 20 (1991), 3-12. · Zbl 0747.93033
[14] A. Vaněček: Control System Theory. (In Czech with extended summary in English.) Academia, Prague 1990.
[15] A. Vaněček, S. Čelikovský: Wrapped eigenstructure of chaos. Kybernetika 29 (1993), 73-79. · Zbl 0802.34053
[16] A. Vaněček, S. Čelikovský: Control Systems. From Linear Analysis to Chaos Synthesis. Prentice/Hall Int., to be published. · Zbl 0874.93006
[17] S. Wiggins: Global Bifurcations and Chaos. Springer-Verlag, New York 1988. · Zbl 0661.58001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.