Suppressing or inducing chaos in a model of robot arms and mechanical manipulators

We study the problems of suppressing or inducing chaotic dynamics in a simple model of robot arms and mechanical manipulators, assuming that the unperturbed systems possess multiple non-transverse homoclinic and/or heteroclinic orbits depending on the model parameters. Based on the Melnikov method and numerical computations for Melnikov integrals, fixed points, and turning points, we obtain conditions for chaos suppression and generation. We prove that the initial phase difference Ψ plays an important role in suppressing or inducing chaos in complex systems. Our results indicate that these methods of controlling or inducing chaos can be easily applied to many systems in natural science and engineering.

[1]  K. Yagasaki.  Chaos in a pendulum with feedback control , 1994 .

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

[3]  Lima,et al.  Suppression of chaos by resonant parametric perturbations. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[4]  Shanmuganathan Rajasekar,et al.  Controlling of chaos by weak periodic perturbations in Duffing-van der Pol oscillator , 1993 .

[5]  Kazuyuki Yagasaki.  A simple feedback control system: Bifurcations of periodic orbits and chaos , 1996 .

[6]  Stephen Wiggins,et al.  Global Bifurcations and Chaos , 1988 .

[7]  Azevedo,et al.  Controlling chaos in spin-wave instabilities. , 1991, Physical review letters.

[8]  B. Koch,et al.  Homoclinic and Heteroclinic Bifurcations in rf SQUIDs , 1988 .

[9]  P. Holmes,et al.  Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.

[10]  G. Litak,et al.  VIBRATION OF EXTERNALLY-FORCED FROUDE PENDULUM , 1999 .

[11]  S. Wiggins.  Introduction to Applied Nonlinear Dynamical Systems and Chaos , 1989 .

[12]  A. Wolf,et al.  Determining Lyapunov exponents from a time series , 1985 .

[13]  I. S. Gradshteyn,et al.  Table of Integrals, Series, and Products , 1976 .

[14]  Francis C. Moon,et al.  Criteria for chaos of a three-well potential oscillator with homoclinic and heteroclinic orbits , 1990 .

[15]  S. Shankar Sastry,et al.  Dynamics of the forced Josephson junction circuit: The regions of chaos , 1985 .

[16]  Francisco Balibrea,et al.  Taming Chaos in a Driven Josephson Junction , 2001, Int. J. Bifurc. Chaos.

[17]  Ricardo Chacón.  General results on chaos suppression for biharmonically driven dissipative systems , 1999 .

[18]  Guanrong Chen,et al.  From Chaos To Order Methodologies, Perspectives and Applications , 1998 .