Synchronizing Chaotic attractors of Chua's Canonical Circuit: the Case of Uncertainty in Chaos Synchronization

In this paper, we have studied the dynamics of two identical resistively coupled Chua's canonical circuits and have found that it is strongly affected by initial conditions, coupling strength and the presence of coexisting attractors. Depending on the coupling variable, chaotic synchronization has been observed both numerically and experimentally. Anti-phase synchronization has also been studied numerically clarifying some aspects of uncertainty in chaos synchronization.

[1]  Huang,et al.  Type-II intermittency in a coupled nonlinear oscillator: Experimental observation. , 1987, Physical review. A, General physics.

[2]  Argoul,et al.  Type-II intermittency in a peroidically driven nonlinear oscillator. , 1986, Physical review. A, General physics.

[3]  Anagnostopoulos,et al.  Crisis-induced intermittency in a third-order electrical circuit. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[4]  Lakshmanan,et al.  Drive-response scenario of chaos synchronization in identical nonlinear systems. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[5]  Anagnostopoulos,et al.  Characterization of the attractor governing the neon bulb RC relaxation oscillator. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[6]  L. Chua,et al.  The double scroll family , 1986 .

[7]  Rabinder N Madan,et al.  Chua's Circuit: A Paradigm for Chaos , 1993, Chua's Circuit.

[8]  P. Linsay Period Doubling and Chaotic Behavior in a Driven Anharmonic Oscillator , 1981 .

[9]  Jose Antonio Coarasa Perez,et al.  Direct observation of crises of the chaotic attractor in a nonlinear oscillator , 1983 .

[10]  Leon O. Chua,et al.  CONTROLLING AND SYNCHRONIZATION OF CHAOS IN THE SIMPLEST DISSIPATIVE NON-AUTONOMOUS CIRCUIT , 1995 .

[11]  Kim-Fung Man,et al.  Uncertainty in Chaos Synchronization , 2001, Int. J. Bifurc. Chaos.

[12]  Ioannis M. Kyprianidis,et al.  Chaotic synchronization of three coupled oscillators with ring connection , 2003 .

[13]  Michael Peter Kennedy,et al.  Three steps to chaos. I. Evolution , 1993 .

[14]  L. O. Chua,et al.  The double scroll family. I: Rigorous of chaos. II: Rigorous analysis of bifurcation phenomena , 1986 .

[15]  Leon O. Chua,et al.  Chaos Synchronization in Chua's Circuit , 1993, J. Circuits Syst. Comput..

[16]  A. Cenys,et al.  Hyperchaotic oscillator with gyrators , 1997 .

[17]  L. Chua,et al.  Hyper chaos: Laboratory experiment and numerical confirmation , 1986 .

[18]  L. Chua,et al.  Canonical realization of Chua's circuit family , 1990 .

[19]  Van Buskirk R,et al.  Observation of chaotic dynamics of coupled nonlinear oscillators. , 1985, Physical review. A, General physics.

[20]  R. W. Rollins,et al.  Intermittent transient chaos at interior crises in the diode resonator , 1984 .

[21]  L. Chua,et al.  Experimental hyperchaos in coupled Chua's circuits , 1994 .

[22]  Leon O. Chua,et al.  EXPERIMENTAL SYNCHRONIZATION OF CHAOS USING CONTINUOUS CONTROL , 1994 .

[23]  J. S. deGrassie,et al.  Observation of multiple-valued attractors and crises in a driven nonlinear circuit , 1983 .

[24]  E. Ott,et al.  Blowout bifurcations: the occurrence of riddled basins and on-off intermittency , 1994 .

[25]  Jose Antonio Coarasa Perez,et al.  OBSERVATION OF A POMEAU-MANNEVILLE INTERMITTENT ROUTE TO CHAOS IN A NONLINEAR OSCILLATOR , 1982 .

[26]  L. Chua,et al.  Devil's staircase route to chaos in a non-linear circuit , 1986 .

[27]  Leon O. Chua,et al.  EXPERIMENTAL OBSERVATION OF ANTIMONOTONICITY IN CHUA'S CIRCUIT , 1993 .

[28]  Krishnamurthy Murali,et al.  SYNCHRONIZING CHAOS IN DRIVEN CHUA'S CIRCUIT , 1993 .

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

[30]  Krishnamurthy Murali,et al.  Bifurcation and chaos of the sinusoidally-driven Chua's circuit , 1991 .

[31]  Tambe,et al.  Driving systems with chaotic signals. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[32]  Kazuhiro Fukushima,et al.  Type-III intermittency in a coupled nonlinear LCR circuit , 1988 .

[33]  L. Chua,et al.  Chaos via torus breakdown , 1987 .

[34]  Toshimichi Saito,et al.  A four-dimensional plus hysteresis chaos generator , 1994 .

[35]  L. Chua,et al.  HYPERCHAOTIC ATTRACTORS OF UNIDIRECTIONALLY-COUPLED CHUA’S CIRCUITS , 1994 .

[36]  Ioannis M. Kyprianidis,et al.  Antimonotonicity and Chaotic Dynamics in a Fourth-Order Autonomous nonlinear Electric Circuit , 2000, Int. J. Bifurc. Chaos.

[37]  Leon O. Chua,et al.  Intermittency in a piecewise-linear circuit , 1991 .

[38]  Ioannis M. Kyprianidis,et al.  Synchronization of two resistively coupled nonautonomous and hyperchaotic oscillators , 2003 .

[39]  A. Tamasevicius,et al.  Hyperchaos in Dynamical Systems with a Monoactive Degree of Freedom , 1998 .