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’ func
tional response term is investigated in this article. Boundedness of the system is established. It is also
proved that the system is uniformly persistent or permanent under certain parametric conditions. Model
systems with Holling type II functional response are known to produce chaotic dynamics. Whereas Holling
type III systems are generally stable in nature. It is observed in the present investigation that general
Holling type or rather an intermediate form of type II and type III functional response can stabilize
the system by eliminating chaotic fluctuation. A detailed numerical simulation is carried out to explain
the change of system dynamics from chaotic state to stable state. Stability of the system has also been
illustrated by bifurcation diagrams and Lyapunov exponent method. Empirical results obtained from
several field survey suggest that interaction between species could not be explained properly through
conventional Holling type II or III functional response terms always. A modified non integer type general
functional response terms could be used more effectively to explain the dynamics observed in these types
of systems. Findings of this investigation somehow support this assumption.