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Nature of weak generalized synchronization in chaotically driven maps

Gerhard Keller1, Haider H. Jafri2, and Ram Ramaswamy2,3

  • 1Department of Mathematics, Universität Erlangen-Nürnberg, Cauerstrasse 11, 91058 Erlangen, Germany
  • 2School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India
  • 3University of Hyderabad, Hyderabad 500 046, India

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Phys. Rev. E 87, 042913 – Published 12 April, 2013

DOI: https://doi.org/10.1103/PhysRevE.87.042913

Abstract

Weak generalized synchrony in a drive-response system occurs when the response dynamics is a unique but nondifferentiable function of the drive, in a manner that is similar to the formation of strange nonchaotic attractors in quasiperiodically driven dynamical systems. We consider a chaotically driven monotone map and examine the geometry of the limit set formed in the regime of weak generalized synchronization. The fractal dimension of the set of zeros is studied both analytically and numerically. We further examine the stable and unstable sets formed and measure the regularity of the coupling function. The stability index as well as the dimension spectrum of the equilibrium measure can be computed analytically.

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Phys. Rev. E 87, 042913– Published 12 April, 2013
  • Received 21 December 2012

©2013 American Physical Society

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