International Journal of Modern Computation, Information and Communication Technology
January 2020, Vol. 3, Issue 1, p. 5-11.
Prey-Predator Mathematical System Analysis through Lyapunov Function
Judith J. E. J. Ogal, N. B. Okelo
School of Mathematics, Statistics and Actuarial Science, Jaramogi Oginga Odinga University of Science and Technology,P. O. Box 210-40601, Bondo-Kenya.
*Corresponding author’s e-mail: firstname.lastname@example.org
Pests are very important in crop production especially aphids are important pests which cannot be ignored in agriculture. The damage they cause to these crops as well as loss of yields can be extensive if not contained. However, to contain these pests, it is important to understand its dynamics in relation to its interaction with its natural enemies like the ladybird. In mathematics, the best tool that can be used to understand this prey-predator dynamics is the models which have different variables and parameters that represent the various aspects of the dynamics of the prey-predator system that we are interested in. In this study, we have therefore gone an extra mile to construct sets of mathematical models, by adjusting the function representing the prey-predator interaction.
Keywords: Prey-predator; Dynamics model; Ladybird; Lyapunov Function.
- Bampflyde CJ, Lewis MA. Biological Control through Intraguild Predation: Case Studies in Pest Control, Invasive Species and Range Expansions. Bulletin of Mathematical Biology 2007;69(2):1032-66.
- Carter Dixon AF, Rabbinge R. Cereal Aphid Populations: Biology, Simulation and Prediction. Simulation Monographs 2019;332(1):91-101.
- Dixon AF. Insect Predator–Prey Dynamics: Ladybird Beetles and Biological Control. Cambridge University Press, Cambridge; 2000.
- Hodek I, Honek A. Ecology of Coccinellidae. Kluwer, Dordrecht; 1996.
- Kindlmann P, Vojtě J, Dixon AF. Population Dynamics. Aphids as crop pests. J Appl Math 2017;76(5):311-29.
- Peixolo MS, Barros LC, Bassanezi RC. Predator-prey fuzzy model. Ecological Modelling 2018;214(2):39-44.
- Okelo NB. On Characterization of Various Finite Subgroups of Abelian Groups. International Journal of Modern Computation, Information and Communication Technology2018;1(5):93-8.
- Okelo NB. On Normal Intersection Conjugacy Functions in Finite Groups. International Journal of Modern Computation, Information and Communication Technology 2018;1(6): 111-5.
- Okwany I, Odongo D, and Okelo NB. Characterizations of Finite Semigroups of Multiple Operators. International Journal of Modern Computation, Information and Communication Technology 2018;1(6):116-20.
- Ramesh R, Mariappan R. Generalized open sets in Hereditary Generalized Topological Spaces. J Math Comput Sci 2015;5(2):149-59.
- Wanjara AO. On the Baire’s Category Theorem as an Important Tool in General Topology and Functional Analysis. International Journal of Modern Computation, Information and Communication Technology 2019;2(4):27-31.