ScienceAsia 28 (2002) : 205-215 |doi: 10.2306/scienceasia1513-1874.2002.28.205

Chaos and Control Action in a Kolmogorov Type Model for Food Webs with Harvesting or Replenishment

Yongwimon Lenbury^*, Adoon Pansuwan, Nardtida Tumrasvin

ABSTRACT: In this paper, we apply the feedback decoupling technique to a Kolmogorov type model for three species food webs with harvesting or replenishment. A feedback control law is derived to decouple the effect of predators from prey dynamics. It is found that the necessary and sufficient conditions for the existence of the decoupling control law rely on the persistence of the prey population and the fact that the specific growth rate of prey depends explicitly on the superpredator population density at any moment in time. It is shown that, without any control action of regulated replenishment or harvesting, irregular or chaotic behavior is possible in such a process for certain ranges of the system parameters. This is illustrated by the construction of a bifurcation diagram for a model of a three-species food web with response functions of the Holling type II. To make the system output or variables less sensitive to irregular disturbances, the feedback control technique is applied which produces the desirable effect of stabilizing the system. When such a model is applied to an activated sludge process, the objective of the control action can also be to regulate the inputs in order to obtain satisfactory water quality.

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Department of Mathematics Faculty of Science, Mahidol University, Rama 6 Rd, Bangkok 10400, Thailand.


*Corresponding author, E-mail: scylb@mahidol.ac.th

Received 11 Sep 2001, Accepted 8 Feb 2002