Persistence of Poincaré mappings in functional differential equations (with application to structural stability of complicated behavior)

DOI10.1007/BF02218814zbMath0832.34082MaRDI QIDQ1347230

Bernhard Lani-Wayda

Publication date: 4 April 1995

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

zbMATH Keywords

chaosstructural stabilitydelay differential equationsfunctional differential equationsshadowing lemmatransversal homoclinic orbitsPoincaré mappingshyperbolic fixed pointpseudoorbitblood production model involving delayscomplicated behavior

Mathematics Subject Classification ID

Stability theory of functional-differential equations (34K20) Structural stability and analogous concepts of solutions to ordinary differential equations (34D30)

Related Items (10)

A Shilnikov phenomenon due to state-dependent delay, by means of the fixed point index ⋮ The unstable set of a periodic orbit for delayed positive feedback ⋮ Floquet multipliers and secondary bifurcations in functional differential equations: Numerical and analytical results ⋮ Saddle-node bifurcation of periodic orbits for a delay differential equation ⋮ Hopf bifurcation for retarded functional differential equations and for semiflows in Banach spaces ⋮ Global stability and periodicity in a glucose-insulin regulation model with a single delay ⋮ Chaotic Motion Generated by Delayed Negative Feedback Part II: Construction of Nonlinearities ⋮ Large-amplitude periodic solutions for differential equations with delayed monotone positive feedback ⋮ Configurations of periodic orbits for equations with delayed positive feedback ⋮ Erratic solutions of simple delay equations

Cites Work

• Hyperbolic sets, transversal homoclinic trajectories, and symbolic dynamics for \(C^ 1\)-maps in Banach spaces
• Symbolic dynamics and nonlinear semiflows
• Geometric theory of semilinear parabolic equations
• Homoclinic structures in infinite-dimensional systems
• Chaotic Behaviour in Simple Dynamical Systems
• Stable and Random Motions in Dynamical Systems
• Examples of transverse homoclinic orbits in delay equations
• Homoclinic solution and chaos in
• Period Three Implies Chaos
• Oscillation and Chaos in Physiological Control Systems
• Hyperbolic periodic solutions, heteroclinic connections and transversal homoclinic points in autonomous differential delay equations
• Differentiable dynamical systems
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