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Chaos and adaptive control in two prey, one predator system with nonlinear feedback. (English) Zbl 1127.92040
Summary: We show that continuous time three species prey-predator populations can be asymptotically stabilized using nonlinear feedback control inputs. The necessary feedback control law for the asymptotic stability of this system is obtained. The system appears to exhibit a chaotic behavior for a range of parametric values. The range of the system parameters for which the subsystems converge to limit cycles is determined. The results of some other models in the literature can be obtained as special cases of the present model. Numerical examples and analysis of the results are presented.
MSC:
92D40Ecology
37D45Strange attractors, chaotic dynamics
93B52Feedback control
92D25Population dynamics (general)
37N25Dynamical systems in biology