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 639798, Singapore
Received 24 September 2003
Copyright © 2004 Weihong Huang. 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
where is a
nonlinear map, and and are nonnegative coupling
constants that satisfy the constraint
, for all , . 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.