Formation of Spatio-temporal Patterns in Stochastic Nonlinear Systems

Exploring the complexities of nonlinear dynamics, this book delves into systems exhibiting excitable, oscillatory, and bistable behaviors. It examines how stochastic fluctuations lead to intricate patterns, including moving clusters and inverted waves. The study includes bifurcations and nucleation of spatial structures, alongside methods for determining front velocities in bounded systems. An abstract two-state model illustrates excitable dynamics, with insights into instantaneous and delayed responses. Additionally, it discusses the transport of Brownian particles in oscillating potentials, highlighting synchronization mechanisms for nearly dispersion-less transport.