Nonlinear dynamics of finite perturbation: collapse and revival of spatial patterns

Ghosh, Pushpita ; Sen, Shrabani ; Ray, Deb Shankar (2009) Nonlinear dynamics of finite perturbation: collapse and revival of spatial patterns Physical Review E - Statistical, Nonlinear and Soft Matter Physics, 79 (1). 016206_1-016206_8. ISSN 1539-3755

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Official URL: http://pre.aps.org/abstract/PRE/v79/i1/e016206

Related URL: http://dx.doi.org/10.1103/PhysRevE.79.016206

Abstract

A full-scale nonlinear stability analysis is performed on a reaction-diffusion system that includes a cubic polynomial source term and Cattaneo's modification of Fick's law of diffusion. This modification incorporates the effect of a small, finite relaxation time of flux at the macroscopic level of the description of the process. While linear stability analysis predicts the decay of small wavelength perturbations on a homogeneous steady state for large reaction time, consideration of finite perturbations leads to a spatiotemporal instability, resulting in an interesting phenomenon of periodic collapse and revival of spatial patterns. This instability is relaxation (time) driven, and the time period is determined by self-sustaining oscillations due to the limit cycle of the underlying dynamics. The nonlinear dynamics of finite perturbations may thus be generically different from what is expected from a linear stability analysis.

Item Type:Article
Source:Copyright of this article belongs to The American Physical Society.
ID Code:69934
Deposited On:12 Nov 2011 11:37
Last Modified:12 Nov 2011 11:37

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