From sine waves to square waves in delay equations

DOI10.1017/S0308210500032108zbMath0764.34048MaRDI QIDQ4009958

Wenzhang Huang, Jack K. Hale, Shui-Nee Chow

Publication date: 27 September 1992

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Bifurcation theory for ordinary differential equations (34C23) Functional-differential equations (including equations with delayed, advanced or state-dependent argument) (34K99)

Related Items (18)

Ikeda Hopf bifurcation revisited ⋮ Periodic solutions of singularly perturbed delay equations ⋮ On the complex dynamic behaviour in nonlinear systems with delay ⋮ Slow–fast dynamics of a time-delayed electro-optic oscillator ⋮ Spatio-temporal phenomena in complex systems with time delays ⋮ Bifurcation and control in a neural network with small and large delays ⋮ Oscillations in first-order, continuous-time systems via time-delay feedback ⋮ Spectrum and amplitude equations for scalar delay-differential equations with large delay ⋮ Uniform numerical method for singularly perturbed delay differential equations ⋮ The asymptotic shapes of periodic solutions of a singular delay differential system ⋮ Periodic solutions of a singular differential delay equation with the Farey-type nonlinearity ⋮ Periodic solutions of a singularly perturbed delay differential equation ⋮ QUALITATIVE BEHAVIOR OF SOLUTIONS OF A CERTAIN HYBRID SYSTEM ⋮ Delayed dynamical systems: networks, chimeras and reservoir computing ⋮ Special issue in celebration of Jack K. Hale's 70th birthday. Part 2 of 4 parts ⋮ Stability of square wave periodic solution for singularly perturbed delay differential equations ⋮ Uniform difference method for parameterized singularly perturbed delay differential equations ⋮ A finite difference scheme for a class of singularly perturbed initial value problems for delay differential equations

Cites Work

• Perturbation theory for dual semigroups. I. The sun-reflexive case
• Theory of functional differential equations. 2nd ed
• Global continuation and asymptotic behaviour for periodic solutions of a differential-delay equation
• Singularities of vector fields

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