PMID: 15244654Jul 13, 2004Paper

Coexistence of stable particle and hole solutions for fixed parameter values in a simple reaction diffusion system

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Yumino HayaseHelmut R Brand

Abstract

We present a simple autocatalytic reaction-diffusion model for two variables, which shows for fixed parameter values the simultaneous stable coexistence of particle solutions as well of two types of hole solutions. The associated spatially homogeneous system is characterized by the coexistence of one stable fixed point and a stable limit cycle solution. We compare our results to other dissipative systems which have for fixed parameters either stable particle or stable hole solutions including the quintic complex Ginzburg-Landau equation and the envelope equation for optical bistability as well as other reaction-diffusion models.

References

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Dec 1, 1996·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·T OhtaR Kobayashi
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Mar 15, 2003·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·O DescalziE Tirapegui
Mar 5, 2004·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Orazio DescalziHelmut R Brand

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Citations

Nov 4, 2015·Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences·Orazio Descalzi, Helmut R Brand
Jul 22, 2009·Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences·Pablo GutiérrezOrazio Descalzi
Dec 31, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Orazio Descalzi, Helmut R Brand
Apr 7, 2010·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Orazio Descalzi, Helmut R Brand
Nov 16, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Orazio DescalziHelmut R Brand
Dec 31, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Orazio Descalzi
Sep 13, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Orazio Descalzi, Helmut R Brand
Sep 28, 2010·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Orazio Descalzi, Helmut R Brand

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