Some Results on Population Dynamics Modelling with Diffusion in a n-Patch Habitat
by
Joydip Dhar
Department of Applied Mathematics, Beant College of Engineering and Technology, Gurdaspur-143521, INDIA

Biotic populations are usually distributed heterogeneously in their habitat, and the distribution itself is patchy. The patchiness also occurs due to geographical and topographical changes in the habitat. In modern times, due to various environmental factors such as industrialization, pollution, deforestation, etc., the animal population are affected all around the world. In this paper, a single species dynamic model with continuous diffusion in a n-patch environment is proposed by assuming the carrying capacities are different in different patches. This model is analyzed in both analytically and numerically. It is shown in both analytically and numerically that there exists a positive, piece-wise monotonic, continuous steady state solution with continuous flux at the interface, in the case of reservoir boundary conditions, that is asymptotically stable in the both local and global cases under certain conditions. All the above results are also true for no-flux (closed habitat) boundary conditions. In the case of uniform equilibrium state it is globally asymptotically stable without any condition.

Date received: March 13, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cadz-66.