Analysis of degenerate hopf bifurcations for a nonlinear model of calcium metabolism

DOI10.1016/0362-546X(89)90049-7zbMath0678.92005MaRDI QIDQ3835343

Philippe Tracqui, Anne-Marie Perault-Staub, Jean-Francois Staub

Publication date: 1989

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

zbMATH Keywords

equilibrium pointsnonlinear modelsglobal bifurcationsbifurcation diagramssingularity theorybirhythmicitydegenerate Hopf bifurcationsbiochemistrycalcium metabolismautocatalytic modelbone interface

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Chemical kinetics in thermodynamics and heat transfer (80A30) Physiological, cellular and medical topics (92Cxx)

Related Items (2)

Homoclinic tangencies in an autocatalytic model of interfacial processes at the bone surface ⋮ Mixed-mode oscillation genealogy in a compartmental model of bone mineral metabolism

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Example of a quadratic system with two cycles appearing in a homoclinic loop bifurcation
• Theoretical study of a two-dimensional autocatalytic model for calcium dynamics at the extracellular fluid-bone interface
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Multiple bifurcation problems for chemical reactors
• Singularities and groups in bifurcation theory. Volume I
• On a four parameter family of planar vector fields
• Qualitative understanding of the Lorenz equations through a well-known second order dynamical system
• Classification and unfoldings of degenerate Hopf bifurcations
• Control of mitosis by a continuous biochemical oscillation: synchronization; spatially inhomogeneous oscillations
• The application of singularity theory to isothermal autocatalytic open systems: the elementary scheme A +mB = (m+ 1)B
• Degenerate Hopf Bifurcation and Nerve Impulse
• A Qualitative Study of the Steady-State Solutions for a Continuous Flow Stirred Tank Chemical Reactor

This page was built for publication: Analysis of degenerate hopf bifurcations for a nonlinear model of calcium metabolism