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From chaos to permanence using control theory (research). (English) Zbl 1440.92054

Acu, Bahar (ed.) et al., Advances in mathematical sciences. AWM research symposium, Houston, TX, USA, April 6–7, 2019. Cham: Springer. Assoc. Women Math. Ser. 21, 85-106 (2020).
Summary: Work by R. F. Costantino et al. [Science 275, No. 5298, 389–391 (1997; Zbl 1225.37103)] and M. Kot et al. [Bull. Math. Biol. 54, No. 4, 619–648 (1992; Zbl 0761.92041)] 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.
For the entire collection see [Zbl 1445.00021].

MSC:

92D25 Population dynamics (general)
92D40 Ecology
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37N25 Dynamical systems in biology
34H05 Control problems involving ordinary differential equations
34H10 Chaos control for problems involving ordinary differential equations
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References:

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