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Zbl 1195.34117
Jiang, Minghui; Shen, Yi; Jian, Jigui; Liao, Xiaoxin
Stability, bifurcation and a new chaos in the logistic differential equation with delay. (English)
[J] Phys. Lett., A 350, No. 3-4, 221-227 (2006). ISSN 0375-9601

Summary: This Letter is concerned with bifurcation and chaos in the logistic delay differential equation with a parameter $r$. The linear stability of the logistic equation is investigated by analyzing the associated characteristic transcendental equation. Based on the normal form approach and the center manifold theory, the formula for determining the direction of Hopf bifurcation and the stability of bifurcation periodic solution in the first bifurcation values is obtained. By theoretical analysis and numerical simulation, we found a new chaos in the logistic delay differential equation.

MSC 2000:: *34K23 Complex (chaotic) behavior of solutions of FDE
34K18 Bifurcation theory of functional differential equations
37D45 Strange attractors, chaotic dynamics

Keywords: logistic delay differential equation; stability; bifurcation; chaos

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Zentralblatt MATH Berlin [Germany]