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Nonlinear dynamics of complicated approaches is an energetic learn box with huge numbers of courses in easy learn, and vast purposes from various fields of technology. Nonlinear dynamics as manifested through deterministic and stochastic evolution versions of complicated habit has entered statistical physics, actual chemistry, biophysics, geophysics, astrophysics, theoretical ecology, semiconductor physics and -optics, and so forth. This box of study has brought on a brand new terminology in technological know-how hooked up with new questions, difficulties, options and strategies. New eventualities have emerged for spatio-temporal constructions in dynamical structures faraway from equilibrium. Their research and attainable keep watch over are exciting and not easy elements of the present learn. The duality of basic and utilized study is a focus of its major attractivity and fascination. easy subject matters and foundations are continually associated with concrete and targeted examples. versions and measurements of advanced nonlinear tactics evoke and galvanize new basic questions that diversify and increase the mathematical ideas and instruments. In go back, new mathematical ways to modeling and research amplify the scope and potency of utilized examine.

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392(6):321-424, 2003. [36] K. Martinez, A. L. Lin, R. Kharrazian, X. Sailer, and H. L. Swinney. Resonance in periodically inhibited reaction-diffusion systems. Physica D, 168:19, 2002. [37] S. C. Muller, T. Plesser, and B. Hess. Two-dimensional spectrophotometry of spiral wave propagation in the Belousov-Zhabotinskii reaction : I. Experiments and digital data representation. Physica D, 24:71, 1987. [38] A. Neiman, P. I. Saparin, and L. Sone. Coherence resonance at noisy precursors of bifurcations in non linear dynamical systems.

1 Synchronization in deterministic systems . . . . . . . . . 2 Effective synchronization in stochastic systems . . . . . . . 3 Discrete models of continuous stochastic dynamics . . . . . . . . 1 The doublewell system - a discrete Markovian description . . . . 2 Excitable dynamics - a phenomenological discrete model . . . . 4 The effective diffusion coefficient and mean frequency in periodically driven renewal processes . . . . . . . , . . . . . . . . . .

5) subjected to a dichotomic periodic driving ( n is some integer) s(t) = c A if t -A if t E E + [nl, ( n ;)I) [(n+ ;)7,( n 1)'T) + Tuning the signal frequency we observe different regions of frequency locking, accompanied by a high number N l o c k of synchronized system cycles, indicating stochastic synchronization (Fig. 1). The following sections are devoted to the calculation of the mean frequency and effective diffusion coefficient in periodically driven bistable and excitable systems. Our approach is based on a modeling of these dynamics as periodic renewal processes, which is presented in the following section.