Local dynamics and bifurcation for a two-dimensional cubic Lotka-Volterra system (I)

Raluca Efrem, Mihaela Sterpu

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. 


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DOI: https://doi.org/10.52846/ami.v50i1.1779