Stability and Andronov-Hopf Bifurcation of a System with Three Time Delays | Zendy

Svetoslav Nikolov | Zendy

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Stability and Andronov-Hopf Bifurcation of a System with Three Time Delays

Author(s) -

Svetoslav Nikolov

Publication year - 2013

Publication title -

journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.252

H-Index - 13

eISSN - 2314-4785

pISSN - 2314-4629

DOI - 10.1155/2013/347071

Subject(s) - mathematics , hopf bifurcation , saddle node bifurcation , limit cycle , bifurcation diagram , biological applications of bifurcation theory , period doubling bifurcation , transcritical bifurcation , infinite period bifurcation , ordinary differential equation , pitchfork bifurcation , bifurcation , stability (learning theory) , mathematical analysis , delay differential equation , limit (mathematics) , bogdanov–takens bifurcation , control theory (sociology) , differential equation , nonlinear system , control (management) , quantum mechanics , machine learning , computer science , management , economics , physics

A general system of three autonomous ordinary differential equations with three discrete time delays is considered. With respect to the delays, we investigate the local stability of equilibria by analyzing the corresponding characteristic equation. Using the Hopf bifurcation theorem, we predict the occurrence of a limit cycle bifurcation for the time delay parameters. Thus, some new mathematical results are obtained. Finally, the above mentioned criteria are applied to a system modelling miRNA regulation.

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