Analytical and Numerical Analysis of Dynamical Behavior in a Nonlinear System with Quadratic Term

Abstract

In this paper, we study a simple nonlinear system where one of the differential equations has quadratic term. The system has no equilibria under certain condition. When it has equilibrium points, the analytical finding shows that they are all unstable. Numerical analysis is used to study the system behavior when the system has no equilibria. We provide some phase portraits, Poincare maps, and bifurcation diagram using local maximum of the system trajectory.