An Anti-Control Scheme for Spiral under Lorenz Chaotic Signals

The Fitzhugh?Nagumo (FHN) equation is used to generate spiral and spatiotemporal chaos. The weak Lorenz chaotic signal is imposed on the system locally and globally. It is found that for the right chaotic driving signal, spiral and spatiotemporal chaos can be suppressed. The simulation results also show that this anti-control scheme is effective so that the system emerges into the stable states quickly after a short duration of chaotic driving (about 50 time units) and the continuous driving keeps the system in a homogeneous state.

[1]  Robert M. May,et al.  Simple mathematical models with very complicated dynamics , 1976, Nature.

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

[3]  David J. Singh,et al.  Theoretical atomic volumes of the light actinides , 2000 .

[4]  Sitabhra Sinha,et al.  Spiral turbulence and spatiotemporal chaos: characterization and control in two excitable media , 2002 .

[5]  S Sinha,et al.  Defibrillation via the elimination of spiral turbulence in a model for ventricular fibrillation. , 2001, Physical review letters.

[6]  P. Hogeweg,et al.  Spiral breakup in a modified FitzHugh-Nagumo model , 1993 .

[7]  Bär,et al.  Statistics of Topological Defects and Spatiotemporal Chaos in a Reaction-Diffusion System. , 1995, Physical review letters.

[8]  Zheng-Ming Ge,et al.  Anti-control of chaos of two-degrees-of-freedom loudspeaker system and chaos synchronization of different order systems , 2004 .

[9]  Jinhu Lu,et al.  A New Chaotic Attractor Coined , 2002, Int. J. Bifurc. Chaos.

[10]  M. Eiswirth,et al.  Turbulence due to spiral breakup in a continuous excitable medium. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[11]  I. Aranson,et al.  Spiral Motion in a Noisy Complex Ginzburg-Landau Equation , 1997, patt-sol/9709005.

[12]  Gunton,et al.  Spiral defect chaos in a model of Rayleigh-Bénard convection. , 1993, Physical review letters.

[13]  J Jalife,et al.  Mechanisms underlying ventricular tachycardia and its transition to ventricular fibrillation in the structurally normal heart. , 2001, Cardiovascular research.

[14]  W. Hongli,et al.  Additive Temporal Coloured Noise Induced Eckhaus Instability in Complex Ginzburg–Landau Equation System , 2004 .

[15]  Guanrong Chen,et al.  YET ANOTHER CHAOTIC ATTRACTOR , 1999 .

[16]  Meron,et al.  Model for spiral wave formation in excitable media. , 1988, Physical review letters.

[17]  Jian-qing Wang,et al.  Unified Understanding of Giant Magnetoresistance Effect and Magnetization in Granular Films with Two-Particle Size Distribution , 2004 .