A simple two-component reaction-diffusion system showing rich dynamic behavior: Spatially homogeneous aspects and selected bifurcation scenarios

Yumino Hayase; Orazio Descalzi; Helmut R. Brand

doi:10.1016/j.physa.2005.05.006

A simple two-component reaction-diffusion system showing rich dynamic behavior: Spatially homogeneous aspects and selected bifurcation scenarios

Yumino Hayase, Orazio Descalzi, Helmut R. Brand^*

^*Corresponding author for this work

Research output: Contribution to journal › Conference article › peer-review

7 Scopus citations

Abstract

We present a simple reaction-diffusion model for two variables. The model was originally designed to have a stable localized solution for a range of parameters as a consequence of the coexistence of a stable limit cycle and a stable fixed point. We classify the spatially homogeneous solutions of the model. In addition we describe several bifurcation scenarios for particle-like solutions as a function of two of the parameters.

Original language	English
Pages (from-to)	19-24
Number of pages	6
Journal	Physica A: Statistical Mechanics and its Applications
Volume	356
Issue number	1
DOIs	https://doi.org/10.1016/j.physa.2005.05.006
State	Published - 1 Oct 2005
Event	Nonequilibrium Statistical Mechanics and Nonlinear Physics (MEDYFINOL'04) - Duration: 2 Dec 2004 → 4 Dec 2004

Bibliographical note

Funding Information:
Y.H. thanks the Alexander von Humboldt-Foundation for partial support. O.D. thanks the Fondecyt (Project 1050660) and FAI (Universidad de los Andes, Project ICIV-001-04) for financial support. H.R.B. thanks the Deutsche Forschungsgemeinschaft for partial support through SFB 481: Polymere und Hybridmaterialien in inneren und äußeren Feldern.

Keywords

Limit cycles
Localized solutions
Particle solutions
Reaction-diffusion systems

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10.1016/j.physa.2005.05.006

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abstract = "We present a simple reaction-diffusion model for two variables. The model was originally designed to have a stable localized solution for a range of parameters as a consequence of the coexistence of a stable limit cycle and a stable fixed point. We classify the spatially homogeneous solutions of the model. In addition we describe several bifurcation scenarios for particle-like solutions as a function of two of the parameters.",

keywords = "Limit cycles, Localized solutions, Particle solutions, Reaction-diffusion systems",

author = "Yumino Hayase and Orazio Descalzi and Brand, {Helmut R.}",

note = "Funding Information: Y.H. thanks the Alexander von Humboldt-Foundation for partial support. O.D. thanks the Fondecyt (Project 1050660) and FAI (Universidad de los Andes, Project ICIV-001-04) for financial support. H.R.B. thanks the Deutsche Forschungsgemeinschaft for partial support through SFB 481: Polymere und Hybridmaterialien in inneren und {\"a}u{\ss}eren Feldern.; Nonequilibrium Statistical Mechanics and Nonlinear Physics (MEDYFINOL'04) ; Conference date: 02-12-2004 Through 04-12-2004",

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doi = "10.1016/j.physa.2005.05.006",

language = "English",

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A simple two-component reaction-diffusion system showing rich dynamic behavior: Spatially homogeneous aspects and selected bifurcation scenarios. / Hayase, Yumino; Descalzi, Orazio; Brand, Helmut R.
In: Physica A: Statistical Mechanics and its Applications, Vol. 356, No. 1, 01.10.2005, p. 19-24.

Research output: Contribution to journal › Conference article › peer-review

TY - JOUR

T1 - A simple two-component reaction-diffusion system showing rich dynamic behavior

T2 - Nonequilibrium Statistical Mechanics and Nonlinear Physics (MEDYFINOL'04)

AU - Hayase, Yumino

AU - Descalzi, Orazio

AU - Brand, Helmut R.

N1 - Funding Information: Y.H. thanks the Alexander von Humboldt-Foundation for partial support. O.D. thanks the Fondecyt (Project 1050660) and FAI (Universidad de los Andes, Project ICIV-001-04) for financial support. H.R.B. thanks the Deutsche Forschungsgemeinschaft for partial support through SFB 481: Polymere und Hybridmaterialien in inneren und äußeren Feldern.

PY - 2005/10/1

Y1 - 2005/10/1

N2 - We present a simple reaction-diffusion model for two variables. The model was originally designed to have a stable localized solution for a range of parameters as a consequence of the coexistence of a stable limit cycle and a stable fixed point. We classify the spatially homogeneous solutions of the model. In addition we describe several bifurcation scenarios for particle-like solutions as a function of two of the parameters.

AB - We present a simple reaction-diffusion model for two variables. The model was originally designed to have a stable localized solution for a range of parameters as a consequence of the coexistence of a stable limit cycle and a stable fixed point. We classify the spatially homogeneous solutions of the model. In addition we describe several bifurcation scenarios for particle-like solutions as a function of two of the parameters.

KW - Limit cycles

KW - Localized solutions

KW - Particle solutions

KW - Reaction-diffusion systems

UR - http://www.scopus.com/inward/record.url?scp=23844549653&partnerID=8YFLogxK

U2 - 10.1016/j.physa.2005.05.006

DO - 10.1016/j.physa.2005.05.006

M3 - Conference article

AN - SCOPUS:23844549653

SN - 0378-4371

VL - 356

SP - 19

EP - 24

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

IS - 1

Y2 - 2 December 2004 through 4 December 2004

ER -

A simple two-component reaction-diffusion system showing rich dynamic behavior: Spatially homogeneous aspects and selected bifurcation scenarios

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