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Study on the Stability and Bifurcation at onset of the Pulse Splitting in Pulse Selfrellication System

【摘要】:正In this paper,a extensive numerical and analytical exploration of the stability of singular homo-clinic stationary solutions and its bifurcations in the one-dimensional Gray-Scott model was carried out.A careful analysis of the scenario of the global bifurcation diagram suggests that the dynamics of self-replicating system is related to a hierarchy structure of folding bifurcation branches in param- eter regions.The numerics suggests the Bogdanov-Takens points together with a presence of a horn of parameter values emanates from the particular codim 2 homoclinic orbit play a central role for global bifurcation of periodic obits and the homoclinic solutions and the complex chaotic dynamics.Numerical simulation also reveals the existence of the modulating two-pulses or multi-pulse,which companying the procedure of pulse self-replicating and splitting in reaction-disusion systems. All the computation in this paper are performed using the continuation code AUTO 2000 software.

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