Chaos and its Controlling Problems for a Nonlinear Circuit System

Abstract:

The complex dynamics characters of a third-order circuit system with nonlinear negative capacitance are studied. The dynamical equation and the state equation of the system are established. By the phase portraits, the motions of the system are studied under the definite parameters. And by bifurcation diagram, the route from periodic motion to chaos is studied under the presented system parameters. Two feedback methods are used to control the chaos of the circuit system. One is an adaptive method and the other is the feedback of states and parameter adjustment method. The phase plane portraits and bifurcation diagram of the controlled system are obtained. The advantages of the two controlled methods are that the collect of the control signals are simple and can put on any time and the chaotic system can be asymptotically stabilized to equilibriums with small control. The orbits of the system can be controlled by these two methods according to our target.

• Periodical: Advanced Materials Research (Volumes 433-440)
• Pages: 7351-7356
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.433-440.7351
• Online since: January 2012
• Authors: Ling Yun Zhu, Xiang Feng Gou, Quan Lei Chen
• Keywords: Bifurcation, Chaos, Chaos Controlling, Nonlinear Circuit, Phase Portrait

References

[1] B. D. Josephson, Possible new effects in superconductive tunneling, Phys. Lett I, 1962, pp.251-253.

[2] Shuang Zhou, An analysis of superconducting acoustic sensor with Josephson junction, Proc. IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY vol. 15, IEEE Press, May. 1995, pp.2694-2697.

DOI: 10.1109/77.403146

[3] Shafranjuk Serhii , B. John and Ketterson, Optimization of the double-barrier Josephson junction switching dynamics, Proc. IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, IEEE press, Dec. 2004, pp.13-21.

DOI: 10.1109/tasc.2004.824329

[4] Haochen Du, Hongyin Liao and Shiping Zhou, Bifurcation, chaotic phenomena and control of chaos in a one-dimensional discrete Josephson lattice, Chinese Physics, vol. 12, Nov. 2003, pp.557-561.

DOI: 10.1088/1009-1963/12/5/318

[5] E. Ott, C. Grebogi and J. A. Yorke, Controlling Chaos, Physics Review Letters, Vol. 64, Nov. 1990, pp.1196-1206.

DOI: 10.1103/physrevlett.64.1196

[6] A. Garfinkel, M. L. Spano, W. L. Ditto, et al, Controlling cardiac chaos, Science, vol. 257, Oct., 1992, pp.1230-1235.

DOI: 10.1126/science.1519060

[7] W. L. Ditto, S. N. Rausco and M. L. Spano, Experimental Control of Chaos, Physics Review Letters, vol. 65, Dec. 1990, p.3211.