## Canard explosion of limit cycles in templator models of self-replication mechanisms

Publication: Research - peer-review › Journal article – Annual report year: 2011

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**Canard explosion of limit cycles in templator models of self-replication mechanisms.** / Brøns, Morten.

Publication: Research - peer-review › Journal article – Annual report year: 2011

### Harvard

*Journal of Chemical Physics*, vol 134, no. 14, pp. 144105., 10.1063/1.3577998

### APA

*Journal of Chemical Physics*,

*134*(14), 144105. 10.1063/1.3577998

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### MLA

*Journal of Chemical Physics*. 2011, 134(14). 144105. Available: 10.1063/1.3577998

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### Bibtex

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### RIS

TY - JOUR

T1 - Canard explosion of limit cycles in templator models of self-replication mechanisms

AU - Brøns,Morten

PY - 2011

Y1 - 2011

N2 - Templators are differential equation models for self-replicating chemical systems. Beutel and Peacock-López [J. Chem. Phys. 126, 125104 (2007)]10.1063/1.2716396 have numerically analyzed a model for a cross-catalytic self-replicating system and found two cases of canard explosion, that is, a substantial change of amplitude of a limit cycle over a very short parameter interval. We show how the model can be reduced to a two-dimensional system and how canard theory for slow-fast equations can be applied to yield analytic information about the canard explosion. In particular, simple expressions for the parameter value where the canard explosion occurs are obtained. The connection to mixed-mode oscillations also observed in the model is briefly discussed. © 2011 American Institute of Physics.

AB - Templators are differential equation models for self-replicating chemical systems. Beutel and Peacock-López [J. Chem. Phys. 126, 125104 (2007)]10.1063/1.2716396 have numerically analyzed a model for a cross-catalytic self-replicating system and found two cases of canard explosion, that is, a substantial change of amplitude of a limit cycle over a very short parameter interval. We show how the model can be reduced to a two-dimensional system and how canard theory for slow-fast equations can be applied to yield analytic information about the canard explosion. In particular, simple expressions for the parameter value where the canard explosion occurs are obtained. The connection to mixed-mode oscillations also observed in the model is briefly discussed. © 2011 American Institute of Physics.

KW - Two-dimensional systems

KW - Delta sigma modulation

KW - Parameter intervals

KW - Differential equation model

KW - Limit cycle

KW - Explosions

KW - Differential equations

KW - Simple expression

KW - Canard explosion

KW - Self-replication mechanism

KW - Self-replicating system

KW - Chemical systems

KW - Explosives

KW - Mixed mode oscillations

U2 - 10.1063/1.3577998

DO - 10.1063/1.3577998

M3 - Journal article

VL - 134

SP - 144105

JO - Journal of Chemical Physics

T2 - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 14

ER -