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.
In: Journal of Chemical Physics, Vol. 134, No. 14, 2011, p. 144105.Publication: Research - peer-review › Journal article – Annual report year: 2011
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TY - JOUR
T1 - Canard explosion of limit cycles in templator models of self-replication mechanisms
A1 - Brøns,Morten
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
JO - Journal of Chemical Physics
JF - Journal of Chemical Physics
SN - 00219606
IS - 14
VL - 134
SP - 144105
ER -