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Global stability of a three species predator-prey food chain dynamics. (English) Zbl 1408.37142
Summary: In this paper controlling chaotic dynamics in a three species food chain model with modified Holling type IV functional response is proposed and studied. The system is observed to be dissipative in the positive octant. The global stability of the equilibrium points is analyzed using Routh-Hurwitz criterion and Lyapunov second method. Lyaponuv exponent and bifurcation diagrams are used to study the dynamics of the system. The effect of the death rate in the dynamics of the food chain system is discussed. Moreover, the role of intraspecific competition in the dynamics of the model is investigated theoretically and additionally numerically.
MSC:
37N25 Dynamical systems in biology
92D25 Population dynamics (general)
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