Multi-valued mappings in generalized chaos synchronization

Abstract

The onset of generalized synchronization of chaos in directionally-coupled systems corresponds to the formation of a continuous mapping which enables one to persistently define the state of the response system from the trajectory of the drive system. The recently developed theory of generalized synchronization of chaos deals only with the case where this synchronization mapping is a single-valued function. In this paper, we explore generalized synchronization in a regime where the synchronization mapping can become a multi-valued function. Specifically, we study the properties of the multi-valued mapping which occurs between the drive and response systems when the systems are synchronized with a frequency ratio other than one-to-one, and address the issues of the existence and continuity of such mappings. The basic theoretical framework underlying the considered synchronization regimes is then developed.

12 pages, 10 figures, to appear in Phys. Rev. E

Cited by in corpus (7)

• Fractional dynamics of systems with long-range interaction
• Fractional dynamics of coupled oscillators with long-range interaction
• Detectability of non-differentiable generalized synchrony
• Tsallis' deformation parameter q quantifies the classical-quantum transition
• Emergence of chaotic attractor and anti-synchronization for two coupled monostable neurons
• Generalized synchronization in the presence of dynamical noise and its detection via recurrent neural networks
• Toward A Mathematical Holographic Principle