{"product_id":"numerical-bifurcation-analysis-for-reaction-diffusion-equations-9783540672968","title":"Numerical Bifurcation Analysis for Reaction-Diffusion Equations","description":"\u003cp\u003e • Author(s): Zhen Mei\u003cbr\u003e • Publisher: Springer\u003cbr\u003e • Publisher Imprint: Springer\u003cbr\u003e • BISAC: Differential Equations - Partial\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eReaction-diffusion equations are typical mathematical models in biology, chemistry and physics. These equations often depend on various parame- ters, e. g. temperature, catalyst and diffusion rate, etc. Moreover, they form normally a nonlinear dissipative system, coupled by reaction among differ- ent substances. The number and stability of solutions of a reaction-diffusion system may change abruptly with variation of the control parameters. Cor- respondingly we see formation of patterns in the system, for example, an onset of convection and waves in the chemical reactions. This kind of phe- nomena is called bifurcation. Nonlinearity in the system makes bifurcation take place constantly in reaction-diffusion processes. Bifurcation in turn in- duces uncertainty in outcome of reactions. Thus analyzing bifurcations is essential for understanding mechanism of pattern formation and nonlinear dynamics of a reaction-diffusion process. However, an analytical bifurcation analysis is possible only for exceptional cases. This book is devoted to nu- merical analysis of bifurcation problems in reaction-diffusion equations. The aim is to pursue a systematic investigation of generic bifurcations and mode interactions of a dass of reaction-diffusion equations. This is realized with a combination of three mathematical approaches: numerical methods for con- tinuation of solution curves and for detection and computation of bifurcation points; effective low dimensional modeling of bifurcation scenario and long time dynamics of reaction-diffusion equations; analysis of bifurcation sce- nario, mode-interactions and impact of boundary conditions.\u003c\/p\u003e","brand":"Springer","offers":[{"title":"Hardcover","offer_id":45283998269591,"sku":"9783540672968","price":7345.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9783540672968.webp?v=1769279870","url":"https:\/\/atlanticbooks.com\/products\/numerical-bifurcation-analysis-for-reaction-diffusion-equations-9783540672968","provider":"Atlantic Books","version":"1.0","type":"link"}