UNIFORM PERSISTENCE AND CONTROL OF CHAOS IN A THREE SPECIES FOOD CHAIN MODEL WITH INTERMEDIATE HOLLING TYPE FUNCTIONAL RESPONSE

Complex dynamics of a three species food chain system with ‘general (intermediate) Holling type’ functional response term is investigated in this article. Boundedness of the system is established. It is alsoproved that the system is uniformly persistent or permanent under certain parametric conditions. Modelsystems with Holling type II functional response are known to produce chaotic dynamics. Whereas Hollingtype III systems are generally stable in nature. It is observed in the present investigation that generalHolling type or rather an intermediate form of type II and type III functional response can stabilizethe system by eliminating chaotic fluctuation. A detailed numerical simulation is carried out to explainthe change of system dynamics from chaotic state to stable state. Stability of the system has also beenillustrated by bifurcation diagrams and Lyapunov exponent method. Empirical results obtained fromseveral field survey suggest that interaction between species could not be explained properly throughconventional Holling type II or III functional response terms always. A modified non integer type generalfunctional response terms could be used more effectively to explain the dynamics observed in these typesof systems. Findings of this investigation somehow support this assumption.