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Slowly Modulated Two-Pulse Solutions in the Gray--Scott Model II: Geometric Theory, Bifurcations, and Splitting Dynamics
SIAM Journal on Applied Mathematics
In this second paper, we develop a geometrical method to systematically study the singular perturbed problem associated to slowly modulated two-pulse solutions. It enables one to see that the characteristics of these solutions are strongly determined by the flow on a slow manifold and, hence, also to identify the saddle-node bifurcations and bifurcations to classical traveling waves in which the solutions constructed in part I are created and annihilated. Moreover, we determine the geometricdoi:10.1137/s0036139900372429 fatcat:gmywur5labejpbtuenomj75bpm