Repellers in reaction-diffusion systems (Q1098008)
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scientific article; zbMATH DE number 4036295
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Repellers in reaction-diffusion systems |
scientific article; zbMATH DE number 4036295 |
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Repellers in reaction-diffusion systems (English)
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1987
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The coexistence problem for reaction-diffusion systems is considered. A method for discovering when an invariant set is a repeller in a certain strong sense is given. The main idea is the weakening of the standard requirements for Lyapunov functionals. First, a general result for dynamical systems on a compact metric space is given and then it is applied to the reaction-diffusion systems to obtain a criterion for permanent coexistence. As an application, a three species reaction- diffusion system with the reaction terms of Lotka-Volterra type are discussed.
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coexistence
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reaction-diffusion
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invariant set
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repeller
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Lyapunov functionals
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dynamical systems
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compact metric space
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