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U.E. Vincent^{a, b, ,} , A.N. Njah^a, O. Akinlade^a and A.R.T. Solarin^c

^aDepartment of Physics, University of Agriculture, P.M.B. 2240, Abeokuta, Nigeria

^bDepartment of Physics and Solar Energy, Bowen University, P.M.B 284, Iwo, Nigeria

^cDepartment of Mathematical Sciences, University of Agriculture, P.M.B. 2240, Abeokuta, Nigeria

Received 22 December 2004;

revised 5 June 2005.

Available online 8 August 2005.

Abstract

We show the existence of phase synchronization in bi-directionally coupled deterministic chaotic ratchets. The coupled ratchets were simulated in their chaotic states. A transition from a regime where the phases rotate with different velocities to a synchronous state where the phase difference is bounded was observed as the coupling was increased. In addition, the region of synchronization in which the system is permanently phase locked was identified. In this regime, the transverse Lyapunov exponent corresponding to both phases remain positive. Our calculations show that the transition to a synchronized state occurs via a crisis transition to an attractor filling the whole phase space.

 

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