Dynamical analysis of a Lotka-Volterra learning-process model

A Lotka-Volterra learning-process model was proposed by Monteiro and Notargiacomo in [{it Commum. Nonlinear Sci. Numer. Simulat.} {bf 47}(2017), 416-420] to approach learning process as an interplay between understanding and doubt. They studied the stability of the boundary equilibria and gave some numerical simulations but no further discussion for bifurcations. In this paper, we study the qualitative properties of the interior equilibria and a singular line segment completely. Moreover, we discuss their bifurcations such as transcritical, pitchfork, Hopf bifurcation on isolated equilibria and transcritical bifurcation without parameters on non-isolated equilibria.Finally, we also demonstrate these analytical theory by numerical simulations.