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Large Systems under Neumann Boundary Conditions, Bifurcations

  • Anthony W. Leung
Chapter
Part of the Mathematics and Its Applications book series (MAIA, volume 49)

Abstract

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 [191], [192], [193] and [194], combining graph-theoretic technique with the use of Lyapunov functions. The earlier use of Lyapunov functions to study such reaction-diffusion systems began with [197], [229], [134], [190], 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. [211], [31], and are thus not included here.

Keywords

Lyapunov Function Large System NEUMANN Boundary Neumann Boundary Condition Nonnegative Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 1989

Authors and Affiliations

  • Anthony W. Leung
    • 1
  1. 1.Department of Mathematical SciencesUniversity of CincinnatiCincinnatiUSA

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