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Stability, bifurcation and a new chaos in the logistic differential equation with delay. (English) Zbl 1195.34117
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:
 34K23 Complex (chaotic) behavior of solutions to functional-differential equations 34K18 Bifurcation theory of functional-differential equations 37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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