Spatially periodic steady-state solutions of a reversible system at strong and subharmonic resonances (Q1174192)
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scientific article; zbMATH DE number 8223
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Spatially periodic steady-state solutions of a reversible system at strong and subharmonic resonances |
scientific article; zbMATH DE number 8223 |
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Spatially periodic steady-state solutions of a reversible system at strong and subharmonic resonances (English)
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25 June 1992
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The system of two reaction-diffusion equations \[ u_ t=u_{xx}+1-u- f(u,v),\quad v_ t=dv_{xx}-kv+f(u,v) \leqno (1) \] with \(f(u,v)=uv^ 2/(1+v+v^ 2)\) is considered. The main results contain both numerical integration of the system (1) with various initial conditions (combinations and perturbations of constant steady-state solutions) and application of Arnol'd and Sevryuk's theorems on resonances in reversible systems to the corresponding steady-state system. The results of numerical modelling are compared with bifurcation theory predictions.
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strong resonance
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subharmonic resonance
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Arnol'd and Sevryuk's theorems
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resonances in reversible systems
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steady-state system
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numerical integration of time-dependent systems
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