Singular Hopf-bifurcation in a chemical reaction-diffusion system
نویسندگان
چکیده
منابع مشابه
Bifurcation analysis of chemical reaction mechanisms. II. Hopf bifurcation analysis
Oneand two-parameter Hopf bifurcation behavior is analyzed for several variants of the Citri-Epstein mechanism of the chlorite-iodide reaction. The coefficients of an equation for the amplitude of oscillations (the universal unfolding of the Hopf bifurcation) are evaluated numerically. Local bifurcation diagrams and bifurcation sets are derived from the amplitude equation. Suband supercritical ...
متن کاملA Hopf Bifurcation in a Three-Component Reaction-Diffusion System with a Chemorepulsion
In this paper, we consider a three-component reaction-diffusion system with a chemorepulsion. The purpose of this work is to analyze the chemotactic effects due to the gradient of the chemotactic sensitivity and the shape of the interface. Conditions for existence of stationary solutions and Hopf bifurcation in the interfacial problem as the bifurcation parameters vary are obtained analytically...
متن کاملGlobal dynamics of the smallest chemical reaction system with Hopf bifurcation
The global behavior of solutions is described for the smallest chemical reaction system that exhibits a Hopf bifurcation, discovered in [12]. This three-dimensional system is a competitive system and a monotone cyclic feedback system. The Poincaré–Bendixson theory extends to such systems [2,3,6,8] and a Bendixson criterion exists to rule out periodic orbits [4].
متن کاملHopf bifurcation in a reaction–diffusion equation with distributed delay and Dirichlet boundary condition
The stability and Hopf bifurcation of the positive steady state to a general scalar reaction–diffusion equation with distributed delay and Dirichlet boundary condition are investigated in this paper. The time delay follows a Gamma distribution function. Through analyzing the corresponding eigenvalue problems, we rigorously show that Hopf bifurcations will occur when the shape parameter n ≥ 1, a...
متن کاملChemical Kinetics on Surfaces: A Singular Limit of a Reaction-Diffusion System
We show that chemical kinetics relations can be used to describe processes that involve binding and dissociation reactions that take place on surfaces. From a mathematical perspective, the problem we study is a singular limit of a reaction-diffusion system in which one of the variables concentrates on a lower-dimensional set in the limit, while the other continues to diffuse in a fixed domain.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Applied Mathematics Letters
سال: 1998
ISSN: 0893-9659
DOI: 10.1016/s0893-9659(98)00069-x