Computation, Continuation and Bifurcation Analysis of Periodic Solutions of Delay Differential Equations-Reference-Cited by-同舟云学术

Computation, Continuation and Bifurcation Analysis of Periodic Solutions of Delay Differential Equations

Published:1997-11 Issue:11 Volume:07 Page:2547-2560
ISSN:0218-1274
Container-title:International Journal of Bifurcation and Chaos
language:en
Short-container-title:Int. J. Bifurcation Chaos

Author:

Luzyanina Tatyana¹,Engelborghs Koen²,Lust Kurt²,Roose Dirk²

Affiliation:

1. Institute of Mathematical Problems in Biology, RAS, Pushchino, Moscow, 142292, Russia

2. Department of Computer Science, Katholieke Universiteit Leuven, Celestijnenlaan 200A, B-3001 Heverlee–Leuven, Belgium

Abstract

We present a new numerical method for the efficient computation of periodic solutions of nonlinear systems of Delay Differential Equations (DDEs) with several discrete delays. This method exploits the typical spectral properties of the monodromy matrix of a DDE and allows effective computation of the dominant Floquet multipliers to determine the stability of a periodic solution. We show that the method is particularly suited to trace a branch of periodic solutions using continuation and can be used to locate bifurcation points with good accuracy.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modeling and Simulation,Engineering (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218127497001709

Reference18 articles.

1. Hereditary Control Problems: Numerical Methods Based on Averaging Approximations

2. Periodic Solutions in a Model of Recurrent Neural Feedback

3. Existence of periodic solutions of autonomous functional differential equations

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