Uniqueness and stability of slowly oscillating periodic solutions of delay equations with bounded nonlinearity

DOI10.1007/BF01049098zbMath0743.34080MaRDI QIDQ1181794

Xianwen Xie

Publication date: 27 June 1992

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

zbMATH Keywords

stablefixed point indexdelay equation with small parametermultiplier equationslowly oscillating periodic solution

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Stability theory of functional-differential equations (34K20) Functional-differential equations (including equations with delayed, advanced or state-dependent argument) (34K99)

Related Items (13)

Existence, Uniqueness, and Stability of Slowly Oscillating Periodic Solutions for Delay Differential Equations with Nonnegativity Constraints ⋮ Continuation of solutions and studying delay differential equations via rigorous numerics ⋮ Floquet multipliers and secondary bifurcations in functional differential equations: Numerical and analytical results ⋮ Exit time asymptotics for small noise stochastic delay differential equations ⋮ Stability of synchronous slowly oscillating periodic solutions for systems of delay differential equations with coupled nonlinearity ⋮ Stability of nonlinear waves in a ring of neurons with delays ⋮ Multiple slowly oscillating periodic solutions for $x’(t) = f(x(t-1))$ with negative feedback ⋮ Nonlinear Dynamics in Queueing Theory: Determining the Size of Oscillations in Queues with Delay ⋮ The multiplier equation and its application to \(S\)-solutions of a differential delay equation ⋮ Dichotomy results for delay differential equations with negative Schwarzian derivative ⋮ Recent advances about the uniqueness of the slowly oscillating periodic solutions of Wright's equation ⋮ On the floquet multipliers of periodic solutions to nonlinear functional differential equations ⋮ Desynchronization of large scale delayed neural networks

Cites Work

• Periodic solutions of difference-differential equations
• Theory of functional differential equations. 2nd ed
• The range of periods of periodic solutions of \(x'(t)=-\alpha f(x(t-1))\)
• Global continuation and asymptotic behaviour for periodic solutions of a differential-delay equation
• Characteristic Multipliers and Stability of Symmetric Periodic Solutions of . x   (t) = g(x(t - 1))

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