Effect of the time delay on the stability and instability of the logistic map

Details Effect of the time delay on the stability and instability of the logistic map Effect of the time delay on the stability and instability of the logistic map

2009-08-27

arxiv.org/abs/0908.3970v1

Mathematics

Dynamical Systems

10pages, 3tables

Scientific paper

A proper discretization of the logistic differential equation, which is preserving these two distinct equilibrium solutions and their unstability and stability, suggest that we need to examine the time delay of the logistic map. According to Murray, the effect of delay in models is "usually" to increase the potential for instability. However the word "usually" is really ambiguous. In this paper, we mathematically formulate and prove the two conjectures about stability and instability.

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