Bifurcation properties for a sequence of approximation of delay equations

DOI10.1016/0022-247X(92)90351-DzbMath0767.34050MaRDI QIDQ1206971

Rachid Benkhalti, Ovide Arino

Publication date: 1 April 1993

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

delay differential equationsoscillating solutionapproximation by difference equationsbifurcation of Rabinowitz type

Mathematics Subject Classification ID

Theoretical approximation of solutions to ordinary differential equations (34A45) Bifurcation theory for ordinary differential equations (34C23) Additive difference equations (39A10) Functional-differential equations (including equations with delayed, advanced or state-dependent argument) (34K99)

Cites Work

• Periodic solutions of systems of ordinary differential equations which approximate delay equations
• A classification of the solutions of a difference equation according to their behavior at infinity
• Effective computation of periodic orbits and bifurcation diagrams in delay equations
• Some global results for nonlinear eigenvalue problems
• Periodic solutions for: ẋ(t) = λf(x(t),x(t – 1))
• Systems of Differential Equations that are Competitive or Cooperative II: Convergence Almost Everywhere
• A non-linear difference-differential equation.
• A Hopf bifurcation theorem for difference equations approximating a differential equation