Numerical Study of Biological Problems in a Predator- Prey System: Mathematical biology - Softcover

Chakraborty, Aspriha

Softcover

ISBN 10: 3639098358 ISBN 13: 9783639098358

Publisher: VDM Verlag Dr. Müller, 2008

Synopsis

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 prey-taxis on the dynamics of the population has been examined using three initial conditions, four response functions and three data sets. The stability of the points of equilibria have been established for each model using Routh-Hurwitz conditions and the variational matrix criteria. This has further been verified through numerical simulations. The effect of bifurcation value of the prey-taxis coefficient on the numerical solution has been examined in each case. It has been observed that as the value of the prey-taxis coefficient becomes considerably higher than the bifurcation value, chaotic dynamics develop. As diffusion in predator velocity is incorporated in the system, it returns to a cyclic pattern. A brief study of coexistence of low population densities both with and without prey-taxis has also been done.

About this title

About the Author

Aspriha Chakraborty is currently a PhD student at Swinburne University of Technology, Melbourne, Australia. She completed Masters in February 2006 from the same university. The present work is based on her Masters thesis.

Edition details

• Publisher: VDM Verlag Dr. Müller
• Publication date: 2008
• Language: English
• ISBN 10: 3639098358
• ISBN 13: 9783639098358
• Binding: Paperback
• Number of pages: 164