Bogdanov-Takens bifurcations in the enzyme-catalyzed reaction comprising a branched network
Copyright policy )Bogdanov-Takens bifurcations in the enzyme-catalyzed reaction comprising a branched network
There have been some results on bifurcations of codimension one (such as saddle-node, transcritical, pitchfork) and degenerate Hopf bifurcations for an enzyme-catalyzed reaction system comprising a branched network but no further discussion for bifurcations at its cusp. In this paper we give conditions for the existence of a cusp and compute the parameter curves for the Bogdanov-Takens bifurcation, which induces the appearance of homoclinic orbits and periodic orbits, indicating the tendency to steady-states or a rise of periodic oscillations for the concentrations of the substrate and the product.
- Sichuan University China (People's Republic of)
- Southwest Petroleum University China (People's Republic of)
- Chengdu University of Information Technology China (People's Republic of)
- Southeast University China (People's Republic of)
Bifurcation theory for ordinary differential equations, Hyperbolic singular points with homoclinic trajectories in dynamical systems, bogdanov-takens bifurcation, Bogdanov-Takens bifurcation, Models, Biological, Catalysis, Enzymes, normal form, Oscillometry, Qualitative investigation and simulation of ordinary differential equation models, QA1-939, Linear Models, cusp, Computer Simulation, enzyme-catalyzed reaction, TP248.13-248.65, Mathematics, Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.), Transformation and reduction of ordinary differential equations and systems, normal forms, Algorithms, Allosteric Site, Software, Biotechnology
Bifurcation theory for ordinary differential equations, Hyperbolic singular points with homoclinic trajectories in dynamical systems, bogdanov-takens bifurcation, Bogdanov-Takens bifurcation, Models, Biological, Catalysis, Enzymes, normal form, Oscillometry, Qualitative investigation and simulation of ordinary differential equation models, QA1-939, Linear Models, cusp, Computer Simulation, enzyme-catalyzed reaction, TP248.13-248.65, Mathematics, Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.), Transformation and reduction of ordinary differential equations and systems, normal forms, Algorithms, Allosteric Site, Software, Biotechnology
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