Synchronization problems for unidirectional feedback coupled nonlinear systems
Abstract
In this paper we consider three different synchronization problems consisting in designing a nonlinear feedback unidirectional coupling term for two (possibly chaotic) dynamical systems in order to drive the trajectories of one of them, the slave system, to a reference trajectory or to a prescribed neighborhood of the reference trajectory of the second dynamical system: the master system. If the slave system is chaotic then synchronization can be viewed as the control of chaos; namely the coupling term allows to suppress the chaotic motion by driving the chaotic system to a prescribed reference trajectory. Assuming that the entire vector field representing the velocity of the state can be modified, three different methods to define the nonlinear feedback synchronizing controller are proposed: one for each of the treated problems. These methods are based on results from the small parameter perturbation theory of autonomous systems having a limit cycle, from nonsmooth analysis and from the singular perturbation theory respectively. Simulations to illustrate the effectiveness of the obtained results are also presented.
Cite
@article{arxiv.0710.0004,
title = {Synchronization problems for unidirectional feedback coupled nonlinear systems},
author = {O. Makarenkov and P. Nistri and D. Papini},
journal= {arXiv preprint arXiv:0710.0004},
year = {2007}
}
Comments
To appear in Dyn. Contin. Discrete Impuls. Syst., Ser. A, Math. Anal