Global bifurcation of periodic solutions to some autonomous differential delay equations

DOI10.1016/0096-3003(83)90037-1zbMath0522.34067OpenAlexW1983149441MaRDI QIDQ1055962

Dietmar Saupe

Publication date: 1983

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0096-3003(83)90037-1

zbMATH Keywords

Galerkin schemeglobal continuaautonomous differential delay equationodd-harmonic periodic solutions

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Functional-differential equations (including equations with delayed, advanced or state-dependent argument) (34K99)

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Bifurcations of periodic solutions of delay differential equations ⋮ Super-high-frequency oscillations in a discontinuous dynamic system with time delay ⋮ Morse decompositions for delay-differential equations ⋮ Continuation of solutions and studying delay differential equations via rigorous numerics ⋮ Examples for smooth bifurcation for ⋮ Smooth bifurcation of symmetric periodic solutions of functional differential equations ⋮ Periodic solutions of a differential-delay equation and the fixed point index ⋮ The multiplier equation and its application to \(S\)-solutions of a differential delay equation ⋮ Oscillatory periodic solutions for two differential-difference equations arising in applications ⋮ Global continuation and asymptotic behaviour for periodic solutions of a differential-delay equation ⋮ Differential Delay Equations That Have Periodic Solutions of Long Period ⋮ Wright's equation has no solutions of period four ⋮ Floquet multipliers of symmetric rapidly oscillating solutions of differential delay equations

Cites Work

• Asymptotic analysis of functional differential equations and solutions of long period
• Effective computation of periodic orbits and bifurcation diagrams in delay equations
• Periodic solutions of some nonlinear autonomous functional differential equations
• The range of periods of periodic solutions of \(x'(t)=-\alpha f(x(t-1))\)
• Uniqueness and nonuniqueness of periodic solutions of x'(t)= -g(x(t-1))
• Periodic solutions of nonlinear functional differential equations
• On accelerating PL continuation algorithms by predictor—corrector methods
• Oscillation and Chaos in Physiological Control Systems
• On the Stability of a Periodic Solution of a Differential Delay Equation
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