Effects of convective and dispersive interactions on the stability of two species |
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Authors: | J B Shukla Sunita Verma |
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Institution: | (1) Department of Mathematics, Indian Institute of Technology, Kanpur, India |
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Abstract: | The evolution and local stability of a system of two interacting species in a finite two-dimensional habitat is investigated
by taking into account the effects of self- and cross-dispersion and convection of the species. In absence of cross-dispersion,
an equilibrium state which is stable without dispersion is always stable with dispersion provided that the dispersion coefficients
of the two species are equal. However, when the dispersion coefficients of the two species are different, the possibility
of self-dispersive instability arises. It is also pointed out that the cross-dispersion of species may lead to stability or
instability depending upon the nature and the magnitude of the cross-dispersive interactions in comparison to the self-dispersive
interactions.
The self-convective movement of species increases the stability of the equilibrium state and can stabilize an otherwise unstable
equilibrium state. The effect of cross-convection (in absence of self-dispersion and self-convection) is to stabilize the
equilibrium state in a prey-predator model with positive cross-dispersion coefficients for the prey species. Finally, it is
shown that if the system is stable under homogeneous boundary conditions it remains so under non-homogeneous boundary conditions. |
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Keywords: | |
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