Date of Award

5-2017

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematical Sciences

Committee Member

Dr. Elena Dimitrova, Committee Chair

Committee Member

Dr. Oleg Yordanov

Committee Member

Dr. Eleanor Jenkins

Committee Member

Dr. Brian Dean

Committee Member

Dr. Matthew Macauley

Abstract

Work by Cushing et al. [18] and Kot et al. [60] demonstrate that chaotic behavior does occur in biological systems. We demonstrate that chaotic behavior can enable the survival/thriving of the species involved in a system. We adopt the concepts of persistence/permanence as measures of survival/thriving of the species [35]. We utilize present chaotic behavior and a control algorithm based on [66, 72] to push a non-permanent system into permanence. The algorithm uses the chaotic orbits present in the system to obtain the desired state. We apply the algorithm to a Lotka-Volterra type two-prey, one-predator model from [30], a ratio-dependent one-prey, two-predator model from [35] and a simple prey-specialist predator-generalist predator (for ex: plant-insect pest-spider) interaction model [67] and demonstrate its effectiveness in taking advantage of chaotic behavior to achieve a desirable state for all species involved.

Included in

Mathematics Commons

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