By L. Schimansky-geier, B. Fiedler, J. Kurths, E. Scholl
Nonlinear dynamics of complicated procedures is an lively study box with huge numbers of courses in simple learn, and vast purposes from various fields of technological know-how. Nonlinear dynamics as manifested via deterministic and stochastic evolution types of advanced habit has entered statistical physics, actual chemistry, biophysics, geophysics, astrophysics, theoretical ecology, semiconductor physics and -optics, and so forth. This box of analysis has caused a brand new terminology in technology attached with new questions, difficulties, ideas and strategies. New situations have emerged for spatio-temporal constructions in dynamical platforms faraway from equilibrium. Their research and attainable keep an eye on are fascinating and difficult points of the present learn. The duality of basic and utilized examine is a focus of its major attractivity and fascination. uncomplicated themes and foundations are continually associated with concrete and specified examples. types and measurements of complicated nonlinear procedures evoke and impress new basic questions that diversify and develop the mathematical strategies and instruments. In go back, new mathematical techniques to modeling and research amplify the scope and potency of utilized examine.
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Additional resources for Analysis and Control of Complex Nonlinear Processes in Physics, Chemistry and Biology
For high E (small separation) we find states with clearly one maximum only. We thus find, depending on the noise intensity and the separation of the timescale three qualitatively different regimes. In these regimes differ- 18 X. R. Sailer, V. Beato et al. 5. Stationary probability distribution of the FitzHugh-Nagumo System. Inhibitor noise intensity is varied (given above the panels). 4.  ent combinations of maxima, minima, and saddle points in the stationary probability distribution can be observed.
025. The reduced two state description is illustrated by the gray line: s ( t ) 0. 50 T . Prager and L . Schimansky-Geier In order to simplify the description of this system one neglects the fast dynamics in the potential wells and considers only the transitions from one well to the other which happen on a much slower time scale. Under the assumption that the potential barrier AU between the two wells is large compared t o the noise strength D and the relaxation in the wells is fast compared to the time scale of the jumps between the wells, the transitions can be considered as a rate process.
Haken. Stochastic resonance without external periodic force. Phys. Rev. , 71:807, 1993.  J. Garcia-Ojalvo and L. Schimansky-Geier. Noise-induced spiral dynamics in excitable media. Europhys. , 47:298-303, 1999.  C. W. Gardiner. Handbook of stochastic methods. Springer, Berlin, second edition, 1985.  P. Hanggi and P. Jung. Colored noise in dynamical systems. Adv. Chem. , 89:239, 1995.  H. Hempel, L. Schimansky-Geier, and J. Garcia-Ojalvo. Noise-sustained pulsating patterns and global oscillations in subexcitable media.
Analysis and Control of Complex Nonlinear Processes in Physics, Chemistry and Biology by L. Schimansky-geier, B. Fiedler, J. Kurths, E. Scholl