Shift of critical points in the parametrically modulated Hénon map with coexisting attractors

Abstract We study how the critical point positions change in the parametrically modulated Henon map with coexisting period-1 and period-3 attractors. In particular, a new type of scaling law is found coinciding with that evidenced by laser experiments. We show that resonance phenomena play a crucial role in deformation of attractors and their basins of attraction.

[1]  J. Yorke,et al.  Final state sensitivity: An obstruction to predictability , 1983 .

[2]  A. Pisarchik,et al.  Stabilizing unstable orbits by slow modulation of a control parameter in a dissipative dynamic system , 1998 .

[3]  Eschenazi,et al.  Basins of attraction in driven dynamical systems. , 1989, Physical review. A, General physics.

[4]  R. Seydel.  From Equilibrium to Chaos: Practical Bifurcation and Stability Analysis , 1988 .

[5]  S. Boccaletti,et al.  The control of chaos: theory and applications , 2000 .

[6]  Huw G. Davies,et al.  A period–doubling bifurcation with slow parametric variation and additive noise , 2001, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[7]  Alexander N. Pisarchik.  Dynamical tracking of unstable periodic orbits , 1998 .

[8]  Dynamic Stabilization of Unstable Periodic Orbits in aCO2Laser by Slow Modulation of Cavity Detuning , 1998 .

[9]  Alexander N. Pisarchik,et al.  EXPERIMENTAL CONTROL OF NONLINEAR DYNAMICS BY SLOW PARAMETRIC MODULATION , 1997 .

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

[11]  Alexander N. Pisarchik,et al.  Shift of attractor boundaries in systems with a slow harmonic parameter perturbation , 2001 .

[12]  A N Pisarchik,et al.  Controlling the multistability of nonlinear systems with coexisting attractors. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  M. Hénon,et al.  A two-dimensional mapping with a strange attractor , 1976 .

[14]  Nicholas B. Tufillaro,et al.  Experimental approach to nonlinear dynamics and chaos , 1992, Studies in nonlinearity.