Stability and Bifurcations in a Bank and Small Enterprise Three-Dimensional continuous Time Dynamical System

Abstract
In this paper we study a three-dimensional continuous time Lotka-Volterra dynamical system, that describes the role of government in interactions with banks and small enterprises.
In Italy the main objective of the government’s economic intervention during the Covid19 Emergency was to maintain the usual operations of the bank-enterprise system. We reviewed the effectiveness of the measures introduced in response to lockdowns to avoid a further credit crunch. Through the application of the bifurcation theory we then find evidence that prove the existence of periodic solutions Hopf and zero-Hopf that bifurcate from a saddle-focus into a special region of the parameters space.
In order to find the periodic solutions, a numerical analysis was performed.