[...]... and correlation times and lengths can be considered as independent variables and, subsequently, as new control parameters of the nonlinear dynamics Normally they can be controlled from outside as, via a random light illumination (chemical reactions) [26] or the pump light (lasers) [49] The inclusion of fluctuations in the description of nonlinear systems is done by two approaches [50] On the one hand... Punckt and H H Rotermund 9 Unified approach to feedback-mediated control of spiral waves in excitable media 243 V S Zykov and H Engel 10 Radiative driven instabilities 2 73 M Hegmann and E Sedlmayr 11 Building oscillations bottom up: Elemental time scales of intracellular calcium dynamics 293 R Thul and M Falcke 12 Continuous wavelet spectral analysis of climate dynamics 325 D Maraun, J Kurths and M... Kurths and M , Holschneider 13 Synchronization of complex systems: Analysis and control 347 M.Rosenblum and A Pikovsky 14 Critical states of seismicity - Implications from a physical model for the seismic cycle 371 G Zoller, M Holschneider and J Kurths 15 Predator-prey oscillations, synchronization and pattern formation in ecological systems B Blasius and R Tonjes 397 Contents Xlll Author Index 429... Briimmer, A P Thomas and T Hofer 5 Pattern formation in semiconductors under the influence of time-delayed feedback control and noise 135 oe E Scholl, J Hizanidis, P H v l and G Stegemann 6 Dynamics of coupled semiconductor lasers L Recke, M Wolfrum and S Yanchuk xi 185 Contents xii 7 Trapping of phase fronts and twisted spirals in periodically forced oscillatory media 213 0 Rudzick and A S Makhailov 8... dichotomic) and will give the mean and the correlation function, i.e and Here we reduced to stationary noise sources Without loss of generality the mean is set to zero For the later on considered types of noise this formulation is sufficient to obtain general answers for ensembles and their averages of the stochastic excitable system Thus we can formulate evolution laws for the probability densities and the... noise (cf chapter 1.3.2) and v(t) is part of the phase space one again gets a Fokker-Planck equation for the density P ( z ,y, u, Similarly, one finds in case of the telegraph t) process balance equations for P ( x ,y, A, t ) and P ( x ,y, , A', t ) which are the densities of the two possible values of the noise A and A' They yield a drift term from the deterministic part and B jump part which describes... sums It is only for polynomials f and g that the sums break off at some final value Even if we deal with polynomials and the sums break off we notice that the dynamics of the n-th central moment generally depends on other, higher moments The system of equations 1.29 forms an infinite set of coupled ordinary differential equations It is only for linear functions f and g that the system decouples For... release [12], CR at the onset of a saddlenode-bifurcation of limit cycles [34] and of period-doubling bifurcations period-doubling bifurcation [38], and spatial CR in a spatially extended system near a pattern-forming instability [ll](for a comprehensive review see [35]) To characterize the level of coherence of noise-induced excitations we analyze the time evolution of the activator concentration... er2 = 0.064 In the right panels are shown enlargements of the trajectories plotted on the left side Time scales tp, te and ta are discussed in the next two pages place at random times, then the error associated to tp is of the same order as the mean ISI, so that Rp ~ 1 Thus Rp is a measure of the coherence of the system response and the minimum of Rp(a2) characterizes the optimal noise intensity We... contribution being independent of the deterministic one In case g(x) is a constant the noise acts additively, otherwise it is called multiplicative (parametric) noise and the influence of the noise depends on the actual state x ( t )of the system The solution of eq 1.4 depends on the sample of [ ( t ) Formally one can interprete the latter as a time dependent parameter and the variable x ( t ) is found . class="bi x0 y0 w0 h1" alt="" Analysis and Control of Corn plex Nonlinear Processes in Physics, CHemistry and Biology WORLD SCIENTIFIC LECTURE NOTES IN COMPLEX SYSTEMS Editor-in-Chief:. concrete and precise examples. Models and measurements of complex nonlinear processes evoke and provoke new fundamental questions and diversify and broaden the mathematical concepts and tools Library. World Scientific Lecture Notes in Complex Systems - Vol. 5 ANALYSIS AND CONTROL OF COMPLEX NONLINEAR PROCESSES IN PHYSICS, CHEMISTRY AND BIOLOGY Copyright 0 2007 by World Scientific