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首页> 外文期刊>Journal of Mathematical Biology >MECHANISMS FOR STABILISATION AND DESTABILISATION OF SYSTEMS OF REACTION-DIFFUSION EQUATIONS
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MECHANISMS FOR STABILISATION AND DESTABILISATION OF SYSTEMS OF REACTION-DIFFUSION EQUATIONS

机译:反应扩散方程组的稳定和失稳机理

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摘要

Potential mechanisms for stabilising and destabilising the spatially uniform steady states of systems of reaction-diffusion equations are examined. In the first instance the effect of introducing small periodic perturbations of the diffusion coefficients in a general system of reaction-diffusion equations is studied. Analytical results are proved for the case where the uniform steady state is marginally stable and demonstrate that the effect on the original system of such perturbations is one of stabilisation. Numerical simulations carried out on an ecological model of Levin and Segel (1976) confirm the analysis as well as extending it to the case where the perturbations are no longer small. Spatio-temporal delay is then introduced into the model. Analytical and numerical results are presented which show that the effect of the delay is to destabilise the original system. [References: 13]
机译:研究了用于稳定和破坏反应扩散方程组系统的空间均匀稳态的潜在机制。在第一种情况下,研究了在一般的反应扩散方程组中引入扩散系数的周期性扰动的效果。对于均匀稳态略微稳定的情况,证明了分析结果,并证明了这种扰动对原始系统的影响是稳定化之一。在Levin和Segel(1976)的生态模型上进行的数值模拟证实了该分析并将其扩展到扰动不再很小的情况。然后将时空时延引入模型。分析和数值结果表明,延迟的影响是使原始系统不稳定。 [参考:13]

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