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Discrete Dynamics in Nature and Society
Volume 2004 (2004), Issue 2, Pages 345-356

On the stabilization of internally coupled map lattice systems

Division of Economics, School of Humanities and Social Sciences, Nanyang Technological University, Nanyang Avenue, Singapore, Singapore 639798

Received 24 September 2003

Copyright © 2004 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The adaptive adjustment mechanism is applied to the stabilization of an internally coupled map lattice system defined by xi,t+1=G((1αiβi)xi,t+αixi+1,t+βixi1,t), where f: is a nonlinear map, and α and β are nonnegative coupling constants that satisfy the constraint αi+βi<1, for all x, i=1,2,,n. Sufficient conditions and ranges of adjustment parameters that guarantee the local stability of a generic steady state have been provided. Numerical simulations have demonstrated the effectiveness and efficiency for this mechanism to stabilize the system to a generic unstable steady state or a periodic orbit.