Abstract
We describe a nonlinear feedback functional method for study both of control and synchronization of spatiotemporal chaos. The method is illustrated by the coupled map lattices with five different connection forms. A key issue addressed is to find nonlinear feedback functions. Two large types of nonlinear feedback functions are introduced. The efficient and robustness of the method based on the flexibility of choices of nonlinear feedback functions are discussed. Various numerical results of nonlinear control are given. We have not found any difficulty for study both of control and synchronization using nonlinear feedback functional method. The method can also be extended to time continuous dynamical systems as well as to society problems.
Highlights
We describe a nonlinear feedback functional method for study both of control and synchronization of spatiotemporal chaos
Most control methods for the above various spatially extended systems belong to linear feedback, nonlinear control of spatiotemporal chaos (STC) has been paid attention to recently, such as integrated approach for nonlinear feedback control was presented with the Gray-Scott model for cubic autocatalysis in a flow reactor [21]
We have suggested a method of nonlinear feedback functions (NFF) which has been applied to synchronization of chaos and hyperchaos in higher-dimensional continuous systems as well as spatiotemporal chaos [23]
Summary
"Two fundamental questions dominate future chaos control theories. The first is the problem of controlling higher-dimensional chaos in physical systems The second question has yet to be addressed: the problem of control in a spatiotemporal system" [1]. Control and synchronization of hyperchaos in higher-dimensional systems as well as spatiotemporal chaos (STC) in spatially extended systems have become a much more important and challenging subject. Most control methods for the above various spatially extended systems belong to linear feedback, nonlinear control of STC has been paid attention to recently, such as integrated approach for nonlinear feedback control was presented with the Gray-Scott model for cubic autocatalysis in a flow reactor [21] This subject still calls for new approaches, in which nonlinear feedback control has become a much more important direction both in automatic control as well as in control chaos [22].
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