Controlling chaos for the dynamical system of coupled dynamos

Abstract This work is a tutorial on the different methods to control chaotic behaviour of the coupled dynamos system. Feedback and nonfeedback control techniques are proposed to suppress chaos to unstable equilibrium or unstable periodic solution. The stabilization of unstable fixed point of the chaotic behaviours is achieved also by bounded feedback method. Stability of the controlled systems are studied by Routh–Hurwitz criterion. Nonfeedback method and a derived method based on the delay feedback control are used to control chaos to periodic orbits. Numerical simulation results are included to show the control process of the different methods.

[1]  H. N. Agiza,et al.  On the Analysis of Stability, Bifurcation, Chaos and Chaos Control of Kopel Map , 1999 .

[2]  Kestutis Pyragas.  Control of chaos via extended delay feedback , 1995 .

[3]  Krishnamurthy Murali,et al.  Control of chaos by nonfeedback methods in a simple electronic circuit system and the FitzHugh-Nagumo equation , 1997 .

[4]  H. Lorenz.  Nonlinear Dynamical Economics and Chaotic Motion , 1989 .

[5]  Alvarez-Ramírez.  Nonlinear feedback for controlling the Lorenz equation. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[6]  Ying-Cheng Lai,et al.  Controlling chaos , 1994 .

[7]  Ott,et al.  Controlling chaos using time delay coordinates via stabilization of periodic orbits. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[8]  Goldhirsch,et al.  Taming chaotic dynamics with weak periodic perturbations. , 1991, Physical review letters.

[9]  Shanmuganathan Rajasekar,et al.  Algorithms for controlling chaotic motion: application for the BVP oscillator , 1993 .

[10]  Guanrong Chen,et al.  Controlling Chua's Circuit , 1993, J. Circuits Syst. Comput..

[11]  J. D. Farmer,et al.  Chaotic attractors of an infinite-dimensional dynamical system , 1982 .

[12]  Zhang,et al.  Suppression and creation of chaos in a periodically forced Lorenz system. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[13]  E. Lorenz.  Deterministic nonperiodic flow , 1963 .

[14]  Roy,et al.  Tracking unstable steady states: Extending the stability regime of a multimode laser system. , 1992, Physical review letters.

[15]  S. Narayanan,et al.  Chaos Control by Nonfeedback Methods in the Presence of Noise , 1999 .

[16]  Jackson Ea,et al.  Controls of dynamic flows with attractors. , 1991 .

[17]  Kestutis Pyragas.  Continuous control of chaos by self-controlling feedback , 1992 .

[18]  Peter A. Cook,et al.  Nonlinear dynamical systems , 1986 .

[19]  Singer,et al.  Controlling a chaotic system. , 1991, Physical review letters.

[20]  Dressler,et al.  Controlling chaos using time delay coordinates. , 1992, Physical review letters.

[21]  Guanrong Chen,et al.  On some controllability conditions for chaotic dynamics control , 1997 .

[22]  Rajasekar.  Controlling of chaotic motion by chaos and noise signals in a logistic map and a Bonhoeffer-van der Pol oscillator. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[23]  M. M. El-Dessoky,et al.  Controlling chaotic behaviour for spin generator and Rossler dynamical systems with feedback control , 2001 .