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2010•Journal of Hunan UniversityRequires access

Frequency Domain Analysis of the Hopf Bifurcation of a Logistic Model with Delay

Maoxin Liao

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Abstract

A logistic model with delay was investigated.By choosing the delay τ as a bifurcation parameter,we show that Hopf bifurcation can occur when τ passes a sequence of critical values.This means that a family of periodic solutions bifurcates from the equilibrium when the bifurcate parameter exceeds a critical value.Some numerical simulations are given to justify the results of the analysis.

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What this paper is about

A logistic model with delay was investigated.By choosing the delay τ as a bifurcation parameter,we show that Hopf bifurcation can occur when τ passes a sequence of critical values.This means that a family of periodic solutions bifurcates from the equilibrium when the bifurcate parameter exceeds a critical value.Some numerical simulations are given to justify the results of the analysis.

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Available abstract

A logistic model with delay was investigated.By choosing the delay τ as a bifurcation parameter,we show that Hopf bifurcation can occur when τ passes a sequence of critical values.This means that a family of periodic solutions bifurcates from the equilibrium when the bifurcate parameter exceeds a critical value.Some numerical simulations are given to justify the results of the analysis.

Key concepts: Hopf bifurcation, Bifurcation, Bifurcation diagram, Mathematics, Period-doubling bifurcation, Transcritical bifurcation, Bogdanov–Takens bifurcation, Saddle-node bifurcation

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