A singular bioeconomic model with diffusion and time delay |
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Authors: | Qingling Zhang Xue Zhang Chao Liu |
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Institution: | (1) Department of Applied Mathematics, Modelling Biomedical Systems Research Group, National University of Science and Technology, P. O. Box AC 939 Ascot, Bulawayo, Zimbabwe;(2) Department of Mathematics and Applied Mathematics, University of Venda, Thohoyandou, South Africa |
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Abstract: | This paper studies a prey-predator singular bioeconomic system with time delay and diffusion, which is described by differential-algebraic
equations. For this system without diffusion, there exist three bifurcation phenomena: Transcritical bifurcation, singularity
induced bifurcation, and Hopf bifurcation. Compared with other biological systems described by differential equations, singularity
induced bifurcation only occurs in singular system and usually links with the expansion of population. When the diffusion
is present, it is shown that the positive equilibrium point loses its stability at some critical values of diffusion rate
and periodic oscillations occur due to the increase of time delay. Furthermore, numerical simulations illustrate the effectiveness
of results and the related biological implications are discussed. |
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Keywords: | |
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