Abstract
A two-dimensional cubic Lotka-Volterra system depending on two parameters is considered. Local dynamics in a neighbourhood of the origin of the phase plane, when the parameters lay in a sufficiently small neighbourhood of the origin, is investigated. The study is performed when some additional hypotheses on the coefficients are satisffied. From one up to four different equilibria and several types of codimension one local bifurcations are found. For each of the identified cases, bifurcation diagrams are given.
Subject
Computer Science Applications,General Mathematics
Reference22 articles.
1. "[1] S. N. Chow, C. Li, D. Wang, Normal Forms and Bifurcation of Planar Vector Fields, Cambridge University Press, Cambridge and New York, 1994.
2. [2] D. Greenhalgh, Q. Khan, F. Al-Kharousi, Eco-epidemiological model with fatal disease in the prey, Nonlinear Anal. RWA 53 (2020), 103072. DOI: 10.1016/j.nonrwa.2019.103072
3. [3] Y.A. Kuznetsov, Elements of Applied Bifurcation Theory (Second Edition), Appl. Math. Sci. vol. 112, Springer-Verlag, New York, 2004.
4. [4] N. G. Lloyd, J. M. Pearson, E Saez, I. Szanto, A cubic Kolmogorov system with six limit cycles, Computers & Mathematics with Applica- tions 44 (2002), Issues 3-4, 445-455. DOI: 10.1016/S0898-1221(02)00161-X
5. [5] F. Brauer, C. Castillo-Chavez, Mathematical Models in Population Biology and Epidemiology, Springer-Verlag, Heidelberg, 2000.