Bifurcation from a 3-D hysteresis piecewise-constant circuit

We propose a 3-D hysteresis piecewise-constant circuit. The circuit consists of linear capacitors and nonlinear voltage controlled current sources. This circuit is extremely simple, but exhibits interesting bifurcation phenomena. The right-hand side of the state equation is piecewise-constant, hence the system dynamics can be simplified into a piecewise-linear return map. Using the return map, the bifurcation phenomena are clarified almost completely.

[1]  Robert W. Newcomb,et al.  An RC op amp chaos generator , 1983 .

[2]  Enric Fossas,et al.  Study of chaos in the buck converter , 1996 .

[3]  L. Chua,et al.  A universal circuit for studying and generating chaos. II. Strange attractors , 1993 .

[4]  T. Saito,et al.  Chaos from a hysteresis and switched circuit , 1995, Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences.

[5]  James A. Yorke,et al.  Border-collision bifurcations in the buck converter , 1998 .

[6]  Toshimichi Saito,et al.  A dependent switched capacitor A/D converter for Farey series approximation , 2000, 2000 IEEE International Symposium on Circuits and Systems. Emerging Technologies for the 21st Century. Proceedings (IEEE Cat No.00CH36353).

[7]  Toshimichi Saito,et al.  A buck-boost converter controlled by periodic inputs , 2000, 2000 IEEE International Symposium on Circuits and Systems. Emerging Technologies for the 21st Century. Proceedings (IEEE Cat No.00CH36353).

[8]  Shunji Ito,et al.  On unimodal linear transformations and chaos , 1979 .

[9]  D. C. Hamill,et al.  Modeling of chaotic DC-DC converters by iterated nonlinear mappings , 1992 .

[10]  T. Saito,et al.  Hysteresis chaos generator , 1985 .

[11]  James A. Yorke,et al.  Ergodic transformations from an interval into itself , 1978 .

[12]  T. Tsubone,et al.  Manifold Piecewise Constant Systems and Chaos , 1999 .

[13]  M. Branicky.  Multiple Lyapunov functions and other analysis tools for switched and hybrid systems , 1998, IEEE Trans. Autom. Control..