Nonequilibrium potential approach: Local and global stability of stationary patterns in an activator-inhibitor system with fast inhibition

Germán Drazer; Horacio S. Wio

doi:10.1016/S0378-4371(97)00047-2

Nonequilibrium potential approach: Local and global stability of stationary patterns in an activator-inhibitor system with fast inhibition

Germán Drazer, Horacio S. Wio

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

We study the formation and global stability of stationary patterns in a finite one-dimensional reaction-diffusion model of the activator-inhibitor type. The analysis proceeds through the study of the nonequilibrium potential or Lyapunov functional for this system considering the fast inhibitor case and, in order to obtain analytical results, the adoption of a piecewise linear version of the model. We have studied the changes in relative stability among the different patterns as the ratio between the diffusion coefficients is varied and have discussed the meaning of the different contributions to the nonequilibrium potential.

Original language	English (US)
Pages (from-to)	571-585
Number of pages	15
Journal	Physica A: Statistical Mechanics and its Applications
Volume	240
Issue number	3-4
DOIs	https://doi.org/10.1016/S0378-4371(97)00047-2
State	Published - Jun 15 1997
Externally published	Yes

All Science Journal Classification (ASJC) codes

Statistics and Probability
Condensed Matter Physics

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abstract = "We study the formation and global stability of stationary patterns in a finite one-dimensional reaction-diffusion model of the activator-inhibitor type. The analysis proceeds through the study of the nonequilibrium potential or Lyapunov functional for this system considering the fast inhibitor case and, in order to obtain analytical results, the adoption of a piecewise linear version of the model. We have studied the changes in relative stability among the different patterns as the ratio between the diffusion coefficients is varied and have discussed the meaning of the different contributions to the nonequilibrium potential.",

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T2 - Local and global stability of stationary patterns in an activator-inhibitor system with fast inhibition

AU - Drazer, Germán

AU - Wio, Horacio S.

PY - 1997/6/15

Y1 - 1997/6/15

N2 - We study the formation and global stability of stationary patterns in a finite one-dimensional reaction-diffusion model of the activator-inhibitor type. The analysis proceeds through the study of the nonequilibrium potential or Lyapunov functional for this system considering the fast inhibitor case and, in order to obtain analytical results, the adoption of a piecewise linear version of the model. We have studied the changes in relative stability among the different patterns as the ratio between the diffusion coefficients is varied and have discussed the meaning of the different contributions to the nonequilibrium potential.

AB - We study the formation and global stability of stationary patterns in a finite one-dimensional reaction-diffusion model of the activator-inhibitor type. The analysis proceeds through the study of the nonequilibrium potential or Lyapunov functional for this system considering the fast inhibitor case and, in order to obtain analytical results, the adoption of a piecewise linear version of the model. We have studied the changes in relative stability among the different patterns as the ratio between the diffusion coefficients is varied and have discussed the meaning of the different contributions to the nonequilibrium potential.

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JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

SN - 0378-4371

IS - 3-4

ER -

Nonequilibrium potential approach: Local and global stability of stationary patterns in an activator-inhibitor system with fast inhibition

Abstract

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