Volume 66 | Issue 3 | Year 2020 | Article Id. IJMTT-V66I3P507 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I3P507
Peter O. Ojwala, Michael O. Okoya, Robert Obogi, "Lie Symmetry Solutions of Coupled LotkaVolterra Competition-Diffusion Model," International Journal of Mathematics Trends and Technology (IJMTT), vol. 66, no. 3, pp. 39-52, 2020. Crossref, https://doi.org/10.14445/22315373/IJMTT-V66I3P507
[1] Mitul I., Bipul I. and Nurul I., Exact solution of the prey-predator model with diffusion using an expansion method. Applied sciences, 1991, vol. 15
[2] Kot M., Elements of mathematical Ecology, Cambridge University press 2001
[3] Kanel J.I. and Zhou L.I., Existence of Wave Front Solutions and Estimates of Wave Speed for A Competition-Diffusion System. Nonlinear Annalysis, Theory, Methods and Applications, 1996, 27
[4] Omar M. H., Application of Symmetry Methods to Partial Differential Equations, PhD thesis 2013
[5] Nikolay A. K. and Anastasia S. Z., Analytical properties and exact solutions of the Lotka-volterra competition system 2014
[6] Murray J.D. Mathematical biology. II. Spatial models and biomedical applications Springer-Verlag, 2003
[7] Li-Chang H., Exact travelling wave solutions for diffusive Lotka-Volterra system of two competing species. Japan, J. indust. Appl. Math. 2012, 29
[8] Kanel J. I.,On the wave front solution of a competition-diffusion system in population dynamics 2006
[9] Yuzo H., Travelling wave for a diffusive Lotka-Volterra competition model I: Singular perturbations, Kyoto Ja , 2003
[10] Ahmed S. and Lazer A. L., An Elementary Approach to Travelling Front Solutions to A System of N Competition-Diffusion Equations, Nonlinear Analysis,Theory, Methods and Applications, 1991, 16.
[11] Wei F., Coexistence, stability, and Limiting Behavior in a One-Predator-Two-Prey Model, Academic Press, Inc, 1993
[12] Kan-On Y., Fisher wave fronts for the Latka-Volterr competition model with diffusive, nonlinear analysis 1997, TMP 28.
[13] Hosono Y, Singular pururbation analysis of travelling waves for Lotka-Volterra competition models, Numerical and Applied Mathematics, Part II, Baltzer, Basel ,1989
[14] Gardner R. A., Existence and stability of travelling wave solution of competition model: a degree theoretic approach, Journal of Differential Equations, 1982, 44.
[15] Morita Y. and Tachibana K., An entire solution to Lotka-Volterra competition-diffusion equation, SIAM Journal on Mathematical Analysis, 2009, 40.
[16] Guo J. S and Wu C. H., Entire solutions for a two-component competition system in Lattice, Tohoku Math. J., 2010, 62
[17] Wang M. and Li G., Entire solutions of a diffusive and competitive Lotka-Volterra type system with nonlocal delays, Nonlinearity, 2010, 23
[18] Rodrigo M. and Mimera M., Exact solutions of competition-diffusion system, Hiroshma Math. J., 2000, 30
[19] Hydon, P., Symmetry methods for differential equations: A beginner’s guide.Cambridge: Cambridge University Press, 2000
[20] Oliveri F., Lie Symmetries of differential equations:Classical results and recent contributions, 2010,Symmetry open access Journals 2, volume 2, Natal, Durban, South Africa
[21] Olver P. J., Applications of Lie Groups to Differential Equations (2nd Ed.) Springer-Verlag, New York, 1993.
[22] Bluman G. W. and Kumei S., Symmetries and Differential Equations, Springer-Verlag, New York 1989.
[23] Ibragimov N., A Practical Course in Mathematical Modelling. ALGA Publications, Blekinge Institute of Technology,Karlskrona,Sweden 2004