An Efficient, Nonlinear Stability Analysis for Detecting Pattern Formation in Reaction Diffusion Systems

An efficient, nonlinear stability analysis for detecting pattern formation in reaction diffusion systems.

Reaction diffusion systems are often used to study pattern formation in biological systems. However, most methods for understanding their behavior are challenging and can rarely be applied to complex systems common in biological applications. I present a relatively simple and efficient, nonlinear stability technique that greatly aids such analysis when rates of diffusion are substantially diffe...

Pattern formation in reaction-diffusion and reaction-diffusion-convection systems

Pattern formation mechanisms in reaction-diffusion systems.

In systems undergoing chemical reaction and diffusion, a remarkable variety of spatially structured patterns, stationary or moving, local or global, can arise, many of them reminiscent of forms and phenomena seen in living systems. Chemical systems offer the advantage that one can often control the parameters that determine the patterns formed and can thereby probe fundamental issues about patt...

Pattern Formation in Reaction-Diffusion Systems

Reaction-diffusion approach has been used to explain pattern formation arising in neurobiology, chemical physics, population ecology, developmental biology and other fields. Despite its simple structure, a class of reaction-diffusion systems exhibit a lot of spatial and spatio-temporal patterns. Some of these patterns in a reacting and diffusing medium can be often observed by internal layers o...

Cross-diffusion and pattern formation in reaction-diffusion systems.

Cross-diffusion, the phenomenon in which a gradient in the concentration of one species induces a flux of another chemical species, has generally been neglected in the study of reaction-diffusion systems. We summarize experiments that demonstrate that cross-diffusion coefficients can be quite significant, even exceeding "normal," diagonal diffusion coefficients in magnitude in systems that invo...