The logistic Lotka-Volterra predator-prey equations with diffusion based on
Luckinbill's experiment with Didinium nasutum as predator and Paramecium aurelia as prey, have been solved numerically along with a third equation to include
prey taxis in the system. The effect of taxis on the dynamics of the population
has been examined under three different non-uniform initial conditions and four
different response functions of predators. The four response functions are Holling
Type 2 Response, Beddington Type Response or Holling Type 3 Response, a response function involving predator interference and a modified sigmoid response
function. The operator splitting method and forward difference Euler scheme have
been used to solve the differential equations. The stability of the solutions has been
established for each model using Routh - Hurwitz conditions, variational matrix.
This has been further verified through numerical simulations.
The numerical solutions have been obtained both with and without prey-taxis
coefficient. The effect of bifurcation value of prey-taxis coe�cient on the numerical
solution has been examined. It has been observed that as the value of the taxis
coefficient is increased significantly from the bifurcation value chaotic dynamics
develops for each model. The introduction of diffusion in predator velocity in the
system restores it back to normal periodic behaviour.
A brief study of coexistence of low population densities both with and without
prey-taxis has also been done.
| Identifer | oai:union.ndltd.org:ADTP/216567 |
| Date | January 2005 |
| Creators | Chakraborty, Aspriha, achakraborty@swin.edu.au |
| Publisher | Swinburne University of Technology. |
| Source Sets | Australiasian Digital Theses Program |
| Language | English |
| Detected Language | English |
| Rights | http://www.swin.edu.au/), Copyright Aspriha Chakraborty |
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