Large Systems under Neumann Boundary Conditions, Bifurcations
In Sections 7.2 and 7.3, we will give a careful treatment of large parabolic systems of Volterra-Lotka prey-predator type under zero Neumann boundary condition. We follow the methods in , ,  and , combining graph-theoretic technique with the use of Lyapunov functions. The earlier use of Lyapunov functions to study such reaction-diffusion systems began with , , , , and others. The recent results presented here give very general and elegant insight into the problem. Such systems had also been investigated by many others by invariant rectangles and comparison methods as indicated in the notes at the end of this chapter. Results using these other techniques had been summarized in other books, e.g. , , and are thus not included here.
KeywordsLyapunov Function Large System NEUMANN Boundary Neumann Boundary Condition Nonnegative Solution
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