Analysis of a Lotka-Volterra food chain chemostat with converting time delays.

*(English)*Zbl 1198.34167Summary: A model of the food chain chemostat involving predator, prey and growth-limiting nutrients is considered. The model incorporates two discrete time delays in order to describe the time involved in converting processes. The Lotka-Volterra type increasing functions are used to describe the species uptakes. In addition to showing that solutions with positive initial conditions are positive and bounded, we establish sufficient conditions for the (i) local stability and instability of the positive equilibrium and (ii) global stability of the non-negative equilibria. Numerical simulation suggests that the delays have both destabilizing and stabilizing effects, and the system can produce stable periodic solutions, quasi-periodic solutions and strange attractors.

Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.

Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.

##### MSC:

34K20 | Stability theory of functional-differential equations |

92D40 | Ecology |

34K60 | Qualitative investigation and simulation of models involving functional-differential equations |

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\textit{F. Wang} et al., Chaos Solitons Fractals 42, No. 5, 2786--2795 (2009; Zbl 1198.34167)

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