We review experimental and theoretical studies on the design and control of spatiotemporal
behavior in chemical systems. A wide range of approaches have been pursued to control …

The present review summarizes experimental and theoretical work dealing with self-
organized solitary localized structures (LSs) that are observed in spatially extended …

A significant part of this book is based on a graduate course on pattern formation which I
have been teaching during the past two decades in the Physics Department at Ben-Gurion …

The Swift-Hohenberg equation with quadratic and cubic nonlinearities exhibits a remarkable
wealth of stable spatially localized states. The presence of these states is related to a …

The bistable Swift-Hohenberg equation exhibits multiple stable and unstable spatially
localized states of arbitrary length in the vicinity of the Maxwell point between spatially …

We review the properties of optical spatial dissipative solitons (SDS). These are stable, self‐
localized optical excitations sitting on a uniform, or quasi‐uniform, background in a …

The Swift–Hohenberg equation with cubic and quintic nonlinearities exhibits multiple stable
and unstable spatially localized states of arbitrary length in the vicinity of the Maxwell point …

In this work, we analyze the linear stability of singular homoclinic stationary solutions and
spatially periodic stationary solutions in the one-dimensional Gray-Scott model. This stability …

Stable localized roll structures have been observed in many physical problems and model
equations, notably in the one-dimensional (1D) Swift–Hohenberg equation. Reflection …

A new geometrical criterion for the transition to spatio-temporal chaos (STC) arising in the
Gray–Scott model is presented. This is based on the inter-relationship of global bifurcating …