From chaos to permanence using control theory (research)

Abstract

Work by Costantino et al. (Am Assoc Adv Sci 275(5298):389–391, 1997) and Kot et al. (Bull Math Biol 54(4):619–648, 1992) demonstrate that chaotic behavior does occur in biological systems. We show that chaotic behavior can also be used to ensure the survival of the species involved in a system. We adopt the concept of permanence as a measure of survival and take advantage of present chaotic behavior to push a non-permanent system into permanence through a control algorithm. We apply the algorithm to a Lotka-Volterra type two-prey, one-predator model and a food chain model and demonstrate its effectiveness in taking advantage of chaotic behavior to achieve a desirable state for all species involved. In particular, we show that harvesting of the predator is a practical and effective control for insuring the thriving of all species in the system.