Dynamics of a discrete Brusselator model: Escape to infinity and Julia set

Hunseok Kang; Yakov Pesin

doi:10.1007/s00032-005-0036-y

Dynamics of a discrete Brusselator model: Escape to infinity and Julia set

Hunseok Kang
, Yakov Pesin

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

20 Scopus citations

Abstract

We consider a discrete version of the Brusselator Model of the famous Belousov-Zhabotinsky reaction in chemistry. The original model is a reaction-diffusion equation and its discrete version is a coupled map lattice. We study the dynamics of the local map, which is a smooth map of the plane. We discuss the set of trajectories that escape to infinity as well as analyze the set of bounded trajectories - the Julia set of the system.

Original language	English (US)
Pages (from-to)	1-17
Number of pages	17
Journal	Milan Journal of Mathematics
Volume	73
Issue number	1
DOIs	https://doi.org/10.1007/s00032-005-0036-y
State	Published - Oct 2005

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/s00032-005-0036-y

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abstract = "We consider a discrete version of the Brusselator Model of the famous Belousov-Zhabotinsky reaction in chemistry. The original model is a reaction-diffusion equation and its discrete version is a coupled map lattice. We study the dynamics of the local map, which is a smooth map of the plane. We discuss the set of trajectories that escape to infinity as well as analyze the set of bounded trajectories - the Julia set of the system.",

author = "Hunseok Kang and Yakov Pesin",

note = "Funding Information: The work was partially supported by National Science Foundation grant \#DMS-0088971 and U.S.-Mexico Collaborative Research grant 0104675 The article is available online on SpringerLink (www.springerlink.com) using colors instead of greyscales in the pictures.",

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AU - Pesin, Yakov

N1 - Funding Information: The work was partially supported by National Science Foundation grant #DMS-0088971 and U.S.-Mexico Collaborative Research grant 0104675 The article is available online on SpringerLink (www.springerlink.com) using colors instead of greyscales in the pictures.

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N2 - We consider a discrete version of the Brusselator Model of the famous Belousov-Zhabotinsky reaction in chemistry. The original model is a reaction-diffusion equation and its discrete version is a coupled map lattice. We study the dynamics of the local map, which is a smooth map of the plane. We discuss the set of trajectories that escape to infinity as well as analyze the set of bounded trajectories - the Julia set of the system.

AB - We consider a discrete version of the Brusselator Model of the famous Belousov-Zhabotinsky reaction in chemistry. The original model is a reaction-diffusion equation and its discrete version is a coupled map lattice. We study the dynamics of the local map, which is a smooth map of the plane. We discuss the set of trajectories that escape to infinity as well as analyze the set of bounded trajectories - the Julia set of the system.

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Dynamics of a discrete Brusselator model: Escape to infinity and Julia set

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