Heteroclinic bifurcation and singularly perturbed boundary value problems

DOI10.1016/0022-0396(90)90082-ZzbMath0708.34017OpenAlexW2154894922MaRDI QIDQ920256

Xiao-Biao Lin

Publication date: 1990

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-0396(90)90082-z

zbMATH Keywords

periodic boundary conditionsexponential dichotomiesheteroclinic bifurcationssingularly perturbed boundary value problemError estimatesFredholm's alternative

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Singular perturbations for ordinary differential equations (34E15) Asymptotic expansions of solutions to ordinary differential equations (34E05) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Local and nonlocal bifurcation theory for dynamical systems (37G99)

Related Items

Geometric singular perturbations for multiple turning points: invariant manifolds and exchange lemmas, Asymptotic Expansion for Layer Solutions of a Singularly Perturbed Reaction-Diffusion System, The contrast structures for a class of singularly perturbed systems with heteroclinic orbits, Construction and asymptotic stability of structurally stable internal layer solutions, On a class of singular boundary value problems with singular perturbation, Shadowing and Silnikov chaos, Boundary value problems for partial differential equations with exponential dichotomies, On the Application of Geometric Singular Perturbation Theory to Some Classical Two Point Boundary Value Problems, Turning points and traveling waves in Fitzhugh--Nagumo type equations, Transverse intersection of invariant manifolds in singular systems., \(S\)-shaped bifurcation of a singularly perturbed boundary value problem, Chaotic traveling wave solutions in coupled Chua's circuits, Multiple internal layer solutions generated by spatially oscillatory perturbations, Exchange lemmas for singular perturbation problems with certain turning points, Transversal heteroclinic and homoclinic orbits in singular perturbation problems

Cites Work

• Construction and stability analysis of transition layer solutions in reaction-diffusion systems
• A remark on singular perturbation methods
• Heteroclinic orbits for retarded functional differential equations
• Asymptotic methods for relaxation oscillations and applications
• The splitting index for linear differential systems
• An example of bifurcation to homoclinic orbits
• Geometric singular perturbation theory for ordinary differential equations
• Hyperbolicity and chain recurrence
• Existence of dichotomies and invariant splittings for linear differential systems. III
• A geometric approach to singular perturbation problems with applications to nerve impulse equations
• Boundary and interior transition layer phenomena for pairs of second- order differential equations
• Dichotomies in stability theory
• A partial differential equation with infinitely many periodic orbits: Chaotic oscillations of a forced beam
• Exponential dichotomies and transversal homoclinic points
• Transition layers in singular perturbation problems
• Dichotomies and stability in singularly perturbed systems of O.D.E.
• Existence and stability of transition layers
• Multiple Solutions of Two-Point Boundary Value Problems of Neumann Type with a Small Parameter
• Perturbation analysis of an approximation to the Hodgkin-Huxley theory
• Shadowing Lemma and Singularly Perturbed Boundary Value Problems
• ASYMPTOTIC BEHAVIOUR OF SOLUTIONS TO CERTAIN PROBLEMS INVOLVING NON-LINEAR DIFFERENTIAL EQUATIONS CONTAINING A SMALL PARAMETER MULTIPLYING THE HIGHEST DERIVATIVES
• Properties of solutions of ordinary differential equations with small parameters
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