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Mathematical Analysis of a Prey–Predator System: An Adaptive Back-Stepping Control and Stochastic Approach

1
Department of Mathematics, National Institute of Food Technology Entrepreneurship and Management (NIFTEM), HSIIDC Industrial Estate, Kundli 131028, Haryana, India
2
Department of Mathematics, School of Advanced Sciences, VIT, Vellore 632014, Tamil Nadu, India
3
Department of Mathematics, S.A. Engineering College, Chennai 600077, Tamil Nadu, India
4
Departamento de Ciencias Exatas e Naturais, Academia Militar, Av. Conde Castro Guimaraes, 2720-113 Amadora, Portugal
*
Author to whom correspondence should be addressed.
Math. Comput. Appl. 2019, 24(1), 22; https://doi.org/10.3390/mca24010022
Received: 4 December 2018 / Revised: 16 January 2019 / Accepted: 30 January 2019 / Published: 5 February 2019
(This article belongs to the Section Natural Sciences)
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Abstract

In this paper, stochastic analysis of a diseased prey–predator system involving adaptive back-stepping control is studied. The system was investigated for its dynamical behaviours, such as boundedness and local stability analysis. The global stability of the system was derived using the Lyapunov function. The uniform persistence condition for the system is obtained. The proposed system was studied with adaptive back-stepping control, and it is proved that the system stabilizes to its steady state in nonlinear feedback control. The value of the system is described mostly by the environmental stochasticity in the form of Gaussian white noise. We also established some conditions for oscillations of all positive solutions of the delayed system. Numerical simulations are illustrated, and sustained our analytical findings. We concluded that controlled harvesting on the susceptible and infected prey is able to control prey infection. View Full-Text
Keywords: prey–predator system; persistence; adaptive back-stepping control; global stability; stochastic analysis prey–predator system; persistence; adaptive back-stepping control; global stability; stochastic analysis
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Das, K.; Srinivas, M.N.; Madhusudanan, V.; Pinelas, S. Mathematical Analysis of a Prey–Predator System: An Adaptive Back-Stepping Control and Stochastic Approach. Math. Comput. Appl. 2019, 24, 22.

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