2007/09/28 by O. Makarenkov, Oleg Makarenkov, Paolo Nistri +6
Computer Science · Mathematics · Physics and Astronomy · #34C28 #93C15 #93D09 #93D20 #Chaos control and synchronization #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Neural Networks Stability and Synchronization #Nonlinear Dynamics and Pattern Formation #math.CA #msc:34C28 #msc:93C15 #msc:93D09 #msc:93D20
paper · pdf · doi:10.48550/arxiv.0710.0004
To appear in Dyn. Contin. Discrete Impuls. Syst., Ser. A, Math. Anal
arxiv created 2007/09/28 · openalex publication_date 2007/09/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.