Controlling bistability by linear augmentation

Abstract In many bistable oscillating systems only one of the attractors is desired to possessing certain system performance. We present a method to drive a bistable system to a desired target attractor by annihilating the other one. This shift from bistability to monostability is achieved by augmentation of the nonlinear oscillator with a linear control system. For a proper choice of the control function one of the attractors disappears at a critical coupling strength in an control-induced boundary crisis. This transition from bistability to monostability is demonstrated with two paradigmatic examples, the autonomous Chua oscillator and a neuronal system with a periodic input signal.

[1]  Awadhesh Prasad,et al.  Targeting fixed-point solutions in nonlinear oscillators through linear augmentation. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  Ray Brown.  Generalizations of the Chua equations , 1993 .

[3]  Chi-Chuan Hwang,et al.  A linear continuous feedback control of Chua's circuit , 1997 .

[4]  F. Arecchi,et al.  Experimental evidence of subharmonic bifurcations, multistability, and turbulence in a Q-switched gas laser , 1982 .

[5]  Alexander N. Pisarchik,et al.  Control of multistability in a directly modulated diode laser , 2002 .

[6]  Ulrike Feudel,et al.  Complex Dynamics in multistable Systems , 2008, Int. J. Bifurc. Chaos.

[7]  Garima Saxena,et al.  Amplitude death: The emergence of stationarity in coupled nonlinear systems , 2012, 1209.6355.

[8]  G. Dangelmayr,et al.  Learning to control a complex multistable system. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  A N Pisarchik,et al.  Experimental demonstration of attractor annihilation in a multistable fiber laser. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  Yu Jiang.  Trajectory selection in multistable systems using periodic drivings , 1999 .

[11]  A. A. Koronovskii,et al.  Dynamical control in multistable systems , 2004 .

[12]  Goswami,et al.  Annihilation of one of the coexisting attractors in a bistable system , 2000, Physical review letters.

[13]  C. Grebogi,et al.  Multistability and the control of complexity. , 1997, Chaos.

[14]  Guanrong Chen,et al.  Coexisting chaotic attractors in a single neuron model with adapting feedback synapse , 2005 .

[15]  Alexander N. Pisarchik,et al.  Oscillation death in coupled nonautonomous systems with parametrical modulation , 2003 .

[16]  K. Kaneko.  Dominance of Milnor Attractors and Noise-Induced Selection in a Multiattractor System , 1997 .