Critical behavior of the Lyapunov exponent in type-III intermittency

Abstract The critical behavior of the Lyapunov exponent near the transition to robust chaos via type-III intermittency is determined for a family of one-dimensional singular maps. Critical boundaries separating the region of robust chaos from the region where stable fixed points exist are calculated on the parameter space of the system. A critical exponent β expressing the scaling of the Lyapunov exponent is calculated along the critical curve corresponding to the type-III intermittent transition to chaos. It is found that β varies on the interval 0 ⩽ β

[1]  Mario G. Cosenza,et al.  Synchronization and Collective Behavior in Globally Coupled Logarithmic Maps , 1998 .

[2]  K. Honda,et al.  Reconsideration of the renormalization-group theory on intermittent chaos , 1991 .

[3]  Young-Jai Park,et al.  Experimental observation of characteristic relations of type-III intermittency in the presence of noise in a simple electronic circuit. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  M. K. Ali,et al.  Robust chaos in smooth unimodal maps. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  Soumitro Banerjee,et al.  Robust Chaos , 1998, chao-dyn/9803001.

[6]  Renormalization-Group Theory on Intermittent Chaos in Relation to Its Universality , 1991 .

[7]  Hermann Haken,et al.  Attractors of convex maps with positive Schwarzian derivative in the presence of noise , 1984 .

[8]  Scaling Law of the Mean Laminar Length in Intermittent Chaos , 1996 .

[9]  M. P. Païdoussis,et al.  Intermittency transition to chaos in the response of a loosely supported cylinder in an array in cross-flow , 1995 .

[10]  Young-Jai Park,et al.  Characteristic Relations of Type-III Intermittency in an Electronic Circuit , 1998 .

[11]  L. Pellegrini,et al.  Different scenarios in a controlled tubular reactor with a countercurrent coolant , 1993 .

[12]  Y. Pomeau,et al.  Intermittent transition to turbulence in dissipative dynamical systems , 1980 .

[13]  Yoshiro Kondo,et al.  Intermittent Chaos Generated by Logarithmic Map , 1991 .

[14]  Fukushima,et al.  Critical behavior for the onset of type-III intermittency observed in an electronic circuit. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[15]  L. Russo,et al.  Complex dynamics and spatio-temporal patterns in a network of three distributed chemical reactors with periodical feed switching , 2006 .