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• W2894498987 abstract "The diffusion equation fails to offer a satisfactory description of dynamics when the correlation between successive motions of dispersive particle is large. Further, the equation is associated with the pitfall of predicting the infinite propagation speed of the diffusive particles. Both limitations arise as the Brownian picture (on which the equation is based on) does not take into account the inertia of the diffusive particles. This could be overcome by introducing a delay in the diffusive flux. The resultant delay-diffusion equation may be converted to an ordinary differential equation by linearizing the flux with respect to the delay, a technique valid in general for small delays. In this article I show that the condition for a spatial bifurcation induced by diffusive delay in the delay differential model is significantly different from the condition derived in an earlier work modifying the reaction-telegraphic equation based on a microscopic approach. The latter necessitates criteria not realizable in common reaction-diffusion models and therefore effectively rules out such kinds of instability in these models. I show here that the instability condition derived with the original nontruncated version of the delayed reaction-diffusion equation does not impose any constraint on the model kinetics, but only requires the diffusive memory to be large enough. Numerical simulation with three well-known reaction-diffusion models corroborates with the predictions of the linear analysis and ensures the that spatiotemporal structure generated is stable in the long term." @default.
• W2894498987 created "2018-10-05" @default.
• W2894498987 creator A5087343581 @default.
• W2894498987 date "2018-09-24" @default.
• W2894498987 modified "2023-09-24" @default.
• W2894498987 title "Spatiotemporal instability in a diffusively relaxed dynamics" @default.
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• W2894498987 doi "https://doi.org/10.1103/physreve.98.032218" @default.
• W2894498987 hasPublicationYear "2018" @default.
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