Analysis and Control of Complex Nonlinear Processes in by L. Schimansky-geier, B. Fiedler, J. Kurths, E. Scholl

By L. Schimansky-geier, B. Fiedler, J. Kurths, E. Scholl

Nonlinear dynamics of advanced approaches is an energetic study box with huge numbers of courses in simple study, and large purposes from diversified fields of technology. Nonlinear dynamics as manifested via 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 analysis has triggered a brand new terminology in technological know-how attached with new questions, difficulties, suggestions and techniques. New eventualities have emerged for spatio-temporal buildings in dynamical structures faraway from equilibrium. Their research and attainable regulate are exciting and hard points of the present study. The duality of primary and utilized learn is a focus of its major attractivity and fascination. uncomplicated themes and foundations are regularly associated with concrete and specified examples. versions and measurements of advanced nonlinear approaches evoke and impress new primary questions that diversify and develop the mathematical suggestions and instruments. In go back, new mathematical techniques to modeling and research magnify the scope and potency of utilized study.

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Bar, M. Eiswirth, H. H. Rotermund, and G. Ertl. Solitary wave phenomena in an excitable surface reaction. Physical Review Letters, 69:945-948, 1992. [5] V. Beato and H. Engel. Coherence resonance phenomena in an excitable system driven by colored noise. Fluct. , 6:L85-L94, 2006. [6] V. Beato, H. Engel, and L. Schimansky-Geier. Pulse trains propagating through excitable media subjected to external noise. 2006. submitted to PRE. [7] V. Beato, I. Sendifia-Nadal, I. Gerdes, and H. Engel. Noise-induced wave nucleations in an excitable chemical reaction.

44 for varying noise intensity. For low noise the fixed point of (x)is stable. Individual systems spike very rarely and incoherently. For increasing noise these spikes become more frequent until the systems start to move coherently. The spikes of the mean are separated by several small amplitude oscillations. The number of these intermediate oscillations decreases and uninterrupted spiking occurs. For even higher noise intensities the coherence is destroyed again. The individual systems still spike frequently but the mean does not.

Same results with bo = 1-2 shown by the red curve, where the fixed point is a stable node. creases, the coherence of ta increases too, see Fig. 7. Only at moderate noise intensities the excursion time tc starts to get affected by noise. In this regime the excitation loops, that at low noise intensities possess well defined trajectories, loose regularity with increasing noise intensity, compare panels at the bottom of Fig. 6. 2 of Fig. 4. There the trajectories of the noise-induced excitations spread out in the phase space for increasing noise intensity.

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