Contents -- Preface -- 1. Noise-induced effects in excitable systems with local and global coupling X . R. Sailer, V. Beato, L. Schirrmnsky-Geier and H. Engel -- 1.1 Introduction -- 1.2 Excitability: What is it and how can we model it? -- 1.2.1 General concept -- 1.2.2 A simple model - the FitzHugh-Nagumo system -- 1.2.3 The Oregonator model for the light-sensitive Belousov-Zhabotinsky reaction -- 1.3 Stochastic methods -- 1.3.1 Langevin equation -- 1.3.2 Stochastic processes: White and colored noises -- 1.3.3 The Fokker-Planck equation -- 1.3.4 Moment dynamics -- 1.4 Stochastic excitable elements -- 1.4.1 The Langevin approach: Phase portraits under fluctuations -- 1.4.2 The Fokker-Planck approach: Numerical solutions -- 1.4.3 The phenomenon of coherence resonance -- 1.4.4 Coherence resonance with respect to the correlation time -- 1.5 Excitable elements with coupling -- 1.5.1 Local coupling: Noise induced nucleations -- 1.5.2 Propagation of trigger waves in the presence of noise -- 1.5.3 Pattern formation in dichotomously driven, locally coupled FitzHugh- Nagumo systems -- 1.5.4 Global coupling -- References -- 2 . Synchronization in periodically driven discrete systems T. Prager and L. Schimansky-Geier -- 2.1 Introduction -- 2.2 Stochastic synchronization in periodically driven systems -- 2.2.1 Synchronization in deterministic systems -- 2.2.2 Effective synchronization in stochastic systems -- 2.3 Discrete models of continuous stochastic dynamics -- 2.3.1 The doublewell system - a discrete Markovian description -- 2.3.2 Excitable dynamics - a phenomenological discrete model -- 2.4 The effective diffusion coefficient and mean frequency in periodically driven renewal processes -- 2.4.1 System cycles involving driven rate steps -- 2.5 Applications -- 2.5.1 Synchronization in a doublewell system -- 2.5.2 Synchronization in the FHN model.

2.5.3 Controlling molecular motors -- 2.6 Conclusion -- References -- 3. Spiral wave dynamics: Reaction and diffusion versus kinematics B. Fiedler, M. Georgi and N . Jangle -- 3.1 Phenomena -- 3.2 Reaction-diffusion spirals -- 3.2.1 Center manifold reductions -- 3.2.2 Center manifolds in unbounded domains -- 3.2.3 Lattice symmetry -- 3.2.4 Spiral tip dynamics -- 3.2.5 Reduced tip equations for the photosensitive system -- 3.2.6 Pinning versus drifting -- 3.3 Kinematics -- 3.3.1 Curves and tips -- 3.3.2 Rigidly rotating spirals -- 3.3.3 Eikonal meanders and drifts -- 3.4 Concluding remarks -- References -- 4. Cellular calcium oscillations: From bifurcation analysis to experiment A. Z. Politi, L. D. Gaspers, A. Brummer, A. P. Thomas and T. Hofer -- 4.1 Introduction -- 4.2 Background -- 4.3 Identification of feedbacks on IP3 -- 4.3.1 General properties of Ca2+-IP3 oscillators -- 4.3.2 A detailed model for Ca2+-IP3 interactions -- 4.3.3 Expression of an IP3 buffer suppresses Ca2+ oscillations -- 4.4 Physiological role of Ca2+ feedbacks on IP3 metabolism -- 4.4.1 The wide range of oscillation periods is due to interactions of IPS and Ca2+ dynamics -- 4.4.2 Intercellular coupling -- 4.5 Conclusions -- References -- 5. Pattern formation in semiconductors under the influence of time-delayed feedback control and noise E. Scholl, J. Hizanidis, P. Hovel and G. Stegemann -- 5.1 Introduction -- 5.2 Chaos control of domains and fronts in superlattices -- 5.3 Control of noise-induced oscillations in superlattices -- 5.4 Chaos control of spatio-temporal oscillations in resonant tunneling diodes -- 5.5 Noise-induced spatio-temporal patterns in the DBRT -- 5.6 Conclusions -- Acknowledgment -- References -- 6. Dynamics of coupled semiconductor lasers L. Recke, M. Wolfrum and S. Yanchuk -- 6.1. Coupled rate equations model -- 6.2. Structural properties of the model.

6.3. CW solutions in the case of no detuning -- 6.3.1. Dynamics in the synchronization subspace -- 6.3.2. Transverse stability of the synchronous C W solutions -- 6.3.3. Asynchronous C W solutions -- 6.4. Influence of the detuning -- 6.4.1. Stationary states in the presence of detuning -- 6.4.2. Regions of locking -- 6.4.3. Stationary states after the symmetry breaking -- 6.4.4. Self-pulsations -- 6.4.5. Identical amplitude synchronization -- 6.4.6. Inverse amplitude synchronization -- 6.4.7. Chaotic oscillations near Zero-Hopf bifurcation point -- 6.5. The case of a small delay -- 6.6. Three coupled identical lasers -- 6.6.1. Conditions for synchronization of the outer lasers -- 6.6.2. Transition t o chaotic synchronization via blowup of a transversely unstable synchronous invariant set -- 6.7. Arrays of coupled oscillators -- References -- 7. Trapping of phase fronts and twisted spirals in periodi- cally forced oscillatory media O. Rudzick and A . S. Makhailov -- 7.1. Periodically forced oscillatory media -- 7.2. The forced complex Ginzburg-Landau equation -- 7.3. Phase front propagation reversal -- 7.4. Phase approximation -- 7.5 Trapping of phase fronts -- 7.6. Twisted spirals -- References -- 8. Visualizing pitting corrosion on stainless steel M. Domhege, C. Punckt and H. H. Rotermund -- 8.1. Introduction -- 8.2. Background -- 8.3. Mathematical model -- 8.4 Experimental methods -- 8.5. Experimental results and discussion -- 8.6. Conclusion -- References -- 9. Unified approach to feedback-mediated control of spiral waves in excitable media V. S. Zykov and H. Engel -- 9.1. Introduction -- 9.2. Spiral waves under periodic parameter modulation -- 9.2.1. Experimental system and underlying mathematical model -- 9.2.2. Archimedean spiral approximation -- 9.2.3. Resonant drift of a spiral wave under periodic parameter modulation.

9.3. Discrete feedback control -- 9.3.1. Resonance attractor for spiral waves subjected t o one- channel feedback -- 9.3.2. Spiral wave drift near a straight line detector -- 9.3.3. Spiral wave drift near a curved one-dimensional detector -- 9.4. Continuous feedback control -- 9.4.1. Superposition principle for feedback-induced spiral drift -- 9.4.2. Two-point feedback control -- 9.4.3. Global feedback in circular and elliptical domains -- 9.5. Discussion -- References -- 10. Radiative driven instabilities M. Hegmann and E. Sedlmayr -- 10.1. Introduction -- 10.2 Gravitational/thermal instability -- 10.2.1. The Jeans instability -- 10.2.2. Thermal instability -- 10.2.3. Stochastic radiative transfer -- 10.2.3.1. Stochastic description of a turbulent velocity field -- 10.2.3.3. Non-LTE lane formation -- 10.2.4. On the cooling by CO -- 10.2.4.1. The model -- 10.2.4.2. Results -- 10.3. The structure of photon dominated regions -- 10.3.1 Numerical model -- 10.4. Radiative instability of dust formation -- 10.4.1. The instability -- 10.4.2. The model -- 10.4.3. Results -- References -- 11. Building oscillations bottom up: Elemental time scales of intracellular calcium dynamics R. Thul and M. Falcke -- 11.1. Introduction -- 11.2. Ca2+ model -- 11.3. Master equation -- 11.4. Fokker-Planck equations -- 11.5. Escape times -- 11.6. Results -- 11.6.1. Mean first passage time -- 11.6.2. Role of fluctuations -- 11.6.3. Distribution of first pussuye time -- 11.6.4. Continuous Ca2+ model -- 11.7. Discussion -- 11.8. Appendix A: Combinatorics for subunits -- 11.9. Appendix B: Proof of equation (32) -- References -- 12. Continuous wavelet spectral analysis of climate dynamics D. Maraun, J. Kurths and M , Holschneider -- 12.1. Introduction -- 12.2. Continuous wavelet transformation -- 12.3. Gaussian processes defined in the wavelet domain -- 12.3.1. Definitions.

12.3.2. Spectral measures -- 12.3.3. Example -- 12.4. Estimating wavelet spectra -- 12.4.1. Spectral estimators -- 12.4.2. Variance of the wavelet sample spectrum -- 12.4.3. Bias of the wavelet sample spectrum -- 12.4.4. Example -- 12.5. Significance testing -- 12.5.1. Sensitivity vs. Specificity -- 12.5.2. Pointwise testing of the wavelet spectrum -- 12.5.3. Areawise testing of the wavelet spectrum -- 12.5.4. Sensitivity and specificity of the areawise test -- 12.5.5. Testing of covarying power -- 12.6. Conclusions -- References -- 13. Synchronization of complex systems: Analysis and control M. Rosenblum and A. Pikovsky -- 13.1. Introduction -- 13.2. Simplest case: Periodically forced self-sustained oscillator -- 13.2.1. Self-sustained oscillators -- 13.2.2. Entrainment by external force: An example -- 13.2.3. Phase dynamics of a forced oscillator -- 13.3. Globally coupled oscillators -- 13.3.1. Globally coupled ensemble as a model of neural synchrony -- 13.4 Controlling neural synchrony -- 13.5 Conclusion -- References -- 14. Critical states of seismicity - Implications from a physical model for the seismic cycle G. Zoller, M. Holschneider and J. Kurths -- 14.1. Introduction -- 14.2. Modeling seismicity in real fault regions -- 14.2.1. Fault geometry and model framework -- 14.2.2. Plate motion -- 14.2.3. Friction and coseismic stress transfer -- quasidynamic approach -- 14.2.4. Model algorithm -- 14.2.5. Data -- 14.3. Results -- 14.3.1. Frequency-size distributions -- 14.3.2. Temporal occurrence of large earthquakes -- 14.3.3. Aftershocks and foreshocks -- 14.3.4. Accelerating moment release -- 14.4. Summary and conclusions -- References -- 15. Predator-prey oscillations, synchronization and pattern formation in ecological systems B. Blasius and R. Tonjes -- 15.1. Introduction -- 15.2. Predator prey systems and oscillations.

15.2.1. The Lotka-Volterra model - does war favour sharks?.