Spatiotemporal Complexity In The Reaction-diffusion System

Recently, reaction-di?usion systems have been playing a signi?-cant role in di?erent ?elds of science such as chemical reactions, elec-tronic devices, combustion processes neuron structures, population oforganisms etc. The main results are as follows:In Chapter 1, we introduce some background knowledge and thestate of study of reaction-di?usion. In Chapter 2, we give a review ofstability and bifurcation analysis of the Gray-Scott model, and inves-tigate the time evolution of pattern formation controlled by noise inthe Gray-Scott model. Furthermore, we establish an extended Gray-Scott model with time-dependent di?usivity and ?nd that the pat-terns exhibit transition from stripe-spot growth to spot or chaos repli-cation. In Chapter 3, we present a theoretical analysis of evolutionaryprocess that involves organisms distribution and their interaction ofspatially distributed population with self as well as cross-di?usion in aHolling-Tanner predator-prey model, the su?cient conditions for theTuring instability with zero-?ux boundary conditions are obtained,Hopf and Turing bifurcation in a spatial domain is presented, too.Furthermore, we present novel numerical evidence of time evolutionof patterns controlled by self as well as cross-di?usion in the model.And in Chapter 4,we give some discussions and remarks.It will be useful for studying dynamic complexity of the reaction-di?usion systems.