By motivating the fact that discrete predator-prey systems often exhibit chaotic behavior, in this paper, control problems of a class of discrete predator-prey systems are studied.
By examining the stability of an equilibrium associated with the predator-prey system, it is first shown that the harvesting or supplying of predators, whose amount is proportional to the number of predator, is effective for preventing oscillations of populations. It is also shown that if the growth rate of predators is too large and the population of predators at the equilibrium is too large, then populations oscillate and these oscillations are stabilized by the harvesting of predators. On the other hand, if the growth rate of predators is too small, the supplying of predators is effective. The optimal harvesting policy yielding the maximum average harvest of predators is also derived.
Furthermore, by introducing the concept of the invariant domain, the constant rate harvesting investigated here is compared with the constant harvesting, and the former is shown to have an advantage from viewpoints of the conservation of ecosystems.
The validity of theoretical results presented here is demonstrated by numerical experiments with various values of parameters.
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