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Application of Extended Geometrical Criterion to Population Model with Two Time Delays

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  • Suqi Ma

Abstract

Geometrical criterion is a flexible method to be applied to a type of delay differential equations with delay dependent coefficient. The criterion is used to solve roots attribution of the related characteristic equation in complex plane effectively by introducing a new parameter skillfully. An extended geometrical criterion is developed to compute the stability of DDEs with two time delays. It is found that stability switching phenomena arise while equilibrium solution loses its stability and becomes unstable, then retrieve its stability again. Hopf bifurcation and the bifurcating periodic solution is analyzed by applying central manifold reduction method. The novel dynamical behaviors such as periodical solution bifurcating to chaos are discovered by using numerical simulation method.

Suggested Citation

  • Suqi Ma, 2018. "Application of Extended Geometrical Criterion to Population Model with Two Time Delays," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 10(3), pages 63-76, June.
    • Handle: RePEc:ibn:jmrjnl:v:10:y:2018:i:3:p:63
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    More about this item

    Keywords

    Hopf bifurcation; parameter delay dependent; geometrical criterion;
    All these keywords.

    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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