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http://dx.doi.org/10.12941/jksiam.2018.22.179

DENSITY DEPENDENT MORTALITY OF INTERMEDIATE PREDATOR CONTROLS CHAOS-CONCLUSION DRAWN FROM A TRI-TROPHIC FOOD CHAIN  

NATH, BINAYAK (DEPARTMENT OF PHYSICS, MAHADEVANANDA MAHAVIDYALAYA)
DAS, KRISHNA PADA (DEPARTMENT OF MATHEMATICS, MAHADEVANANDA MAHAVIDYALAY)
Publication Information
Journal of the Korean Society for Industrial and Applied Mathematics / v.22, no.3, 2018 , pp. 179-199 More about this Journal
Abstract
The paper explores a tri-trophic food chain model with density dependent mortality of intermediate predator. To analyze this aspect, we have worked out the local stability of different equilibrium points. We have also derived the conditions for global stability of interior equilibrium point and conditions for persistence of model system. To observe the global behaviour of the system, we performed extensive numerical simulations. Our simulation results reveal that chaotic dynamics is produced for increasing value of half-saturation constant. We have also observed trajectory motions around different equilibrium points. It is noticed that chaotic dynamics has been controlled by increasing value of density dependent mortality parameter. So, we conclude that the density dependent mortality parameter can be used to control chaotic dynamics. We also applied basic tools of nonlinear dynamics such as Poincare section and Lyapunov exponent to investigate chaotic behaviour of the system.
Keywords
Food chain; Density dependent mortality; chaos; Poincare map; Lyapunov exponen;
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