Formation of Spatio-temporal Patterns in Stochastic Nonlinear Systems: a Study of Extended Systems with Reference to Abstract Biological Mechanisms

The physical essence of complex structures goes beyond Newton's dynamical laws. In this book systems are investigated which exhibit excitable, oscillatory and bistable behavior as basic modes of nonlinear dynamics. Addition of stochastic fluctuations contribute to the appearance of complex behavior. Bifurcations of local behavior as well as nucleation of spatially extended structures are studied. Typical fronts and spirals appear but also unusual patterns such as moving clusters and inverted waves. Methods are presented to find expressions for front velocities in the presence of system boundaries. An abstract two-state model with two waiting time distributions is considered representing excitable dynamics. Instantaneous and delayed response of the ensemble's response is analyzed. Furthermore transport and diffusion of Brownian particles in a spatio-temporal oscillating potential is discussed. As a cause of nearly dispersion-less transport synchronization mechanisms can be identified.