MULTIPARAMETRIC BIFURCATIONS IN AN ENZYME-CATALYZED REACTION MODEL

DOI10.1142/S0218127405012521zbMath1069.92009OpenAlexW2094615101MaRDI QIDQ5318377

Fernando Fernández-Sánchez, Emilio Freire, Luis Pizarro, Alejandro J. Rodríguez-Luis

Publication date: 26 September 2005

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218127405012521

zbMATH Keywords

homoclinic connectionsenzyme model

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Classical flows, reactions, etc. in chemistry (92E20) Bifurcation theory for ordinary differential equations (34C23) Biochemistry, molecular biology (92C40) Qualitative investigation and simulation of ordinary differential equation models (34C60) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (12)

Local bifurcations of an enzyme-catalyzed reaction system with cubic rate law ⋮ Qualitative analysis and Hopf bifurcation of a generalized Lengyel-Epstein model ⋮ Takens-Bogdanov bifurcations of equilibria and periodic orbits in the Lorenz system ⋮ Computation of all the coefficients for the global connections in the \(\mathbb{Z}_2\)-symmetric Takens-Bogdanov normal forms ⋮ Homoclinic-doubling and homoclinic-gluing bifurcations in the Takens-Bogdanov normal form with D4 symmetry ⋮ Analytical approximation of cuspidal loops using a nonlinear time transformation method ⋮ A nonlinear time transformation method to compute all the coefficients for the homoclinic bifurcation in the quadratic Takens-Bogdanov normal form ⋮ High-Order Analysis of Global Bifurcations in a Codimension-Three Takens–Bogdanov Singularity in Reversible Systems ⋮ Global dynamics of an enzyme-catalyzed reaction system ⋮ Bifurcation Analysis of an Enzyme Reaction System with General Power of Autocatalysis ⋮ Localised spatial structures in the Thomas model ⋮ Local Bifurcations of the Enzyme-Catalyzed Reaction Comprising a Branched Network

Uses Software

• AUTO-86
• PITCON
• DSTool
• HomCont

Cites Work

• Unnamed Item
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• Generalized Hopf Bifurcation and Its Dual Generalized Homoclinic Bifurcation
• The Saddle-Node Separatrix-Loop Bifurcation
• Bifurcations of cuspidal loops
• Unfolding a Point of Degenerate Hopf Bifurcation in an Enzyme-Catalyzed Reaction Model
• Numerical continuation of degenerate homoclinic orbits in planar systems
• Elementary graphics of cyclicity 1 and 2
• NUMERICAL DETECTION AND CONTINUATION OF CODIMENSION-TWO HOMOCLINIC BIFURCATIONS
• A NUMERICAL TOOLBOX FOR HOMOCLINIC BIFURCATION ANALYSIS
• NUMERICAL ANALYSIS AND CONTROL OF BIFURCATION PROBLEMS (I): BIFURCATION IN FINITE DIMENSIONS
• Introduction to Applied Nonlinear Dynamical Systems and Chaos
• Numerical continuation of homoclinic orbits to non-hyperbolic equilibria in planar systems

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