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.
Recommended Citation
Chenthittayil, Sherli Koshy, "Chaos to Permanence - Through Control Theory" (2017). All Dissertations. 2034.
https://tigerprints.clemson.edu/all_dissertations/2034