European Conference - Workshop “Nonlinear Maps and Applications”

doi:10.1088/1742-6596/990/1/011001

Abstract

Efremova L.S.1, Gracio M.C.2, Lopez-Ruiz R.3, Sakbaev V.Zh.4, Stepin A.M.51 National Research University of Nizhni Novgorod, Russia2 University of Evora, CIMA - UE, Portugal3 University of Zaragoza, Spain4 Moscow Institute of Physics and Technology, Dolgoprudny, Russia5 Moscow State University, RussiaRegular European Workshops ”Nonlinear Maps and Applications” (NOMA) are held biannually in those European Universities where successful researchers in the area of nonlinear maps and their applications work.In far 1973 year French scientist Christian Mira organized Colloquium ”Point Mappings and Applications” in the University of Toulouse, where he worked. According to Christian Mira, his mathematical preferences were formed under the influence of works of the founder of the Nizhni Novgorod nonlinear oscillations school A.A. Andronov.

Highlights

Chaotic synchronization is a very important phenomenon in many fields involving mathematical, physical, sociological, physiological, biological or other systems [1, 2, 3, 4]
In this paper we deal with general couplings of two dynamical systems and we study strong generalized synchronization with a particular relationship R between them
In the case of unidirectional or symmetric couplings, this window is presented in terms of the maximum Lyapunov exponent of the systems

Summary

Introduction

Chaotic synchronization is a very important phenomenon in many fields involving mathematical, physical, sociological, physiological, biological or other systems [1, 2, 3, 4]. 3. R-synchronization window Even if a coupling admits generalized synchronization with a particular relationship R, only some values of the coupling strength (or even none) correspond to a coupling that admits a function st such that (xt, yt) = (st, R (st)) is an exponentially stable solution. For a c-family of couplings that admit generalized synchronization with a particular relationship R, we call R-synchronization window, RSW , the set of values of the coupling strength c for which there is a function st such that (xt, yt) = (st, R (st)) is an exponentially stable solution of (1). We note that in both of the previous propositions RSW only depends on f , which means that using an unidirectional or a symmetric coupling in order to obtain an exponentially stable R-synchronization, the values of the coupling strength c that must be used are independent of R. In both cases the width of the RSW is e−μ0 but for a symmetric coupling an exponentially stable R-synchronization is obtained for smaller values of the coupling strength

Examples of the R-synchronization windows

Conclusions