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A Lotka–Volterra type food chain model with stage structure and time delays. (English) Zbl 1096.34055
A three species Lotka-Volterra-type food chain model with mature and immature species and delay is investigated. First, the positivity of the solutions is proved. Then, sufficient conditions for the permanence of the solutions are given. Equilibrium solutions of the system are found. They represent the total annihilation of the system (E0), the annihilation of predators (E1), the annihilation of the top prey only (E2) and the coexistence of all species (E*). Sufficient conditions for the global stability of E1, E2, E* are derived.
A related paper is given by J. F. M. Al-Omari and S. A. Gourley [Nonlinear Anal., Real World Appl. 6, 13–33 (2005; Zbl 1088.34070)].

MSC:
34K25 Asymptotic theory of functional-differential equations
92D25 Population dynamics (general)
34K20 Stability theory of functional-differential equations
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