Stability of Lorenz System at the Second Equilibria Point based on Gardano’s Method

Abstract

Abstract In this paper, stability conditions of the Lorenz system at the second equilibrium point are investigated by applying Gardano’s method where the system has three equilibria points. Most of the previous work focused their studies at the original point. A few studies demonstrated stability of dynamical systems at another equilibria points by use of conventional techniques. However, it is often unclear and based on numerical methods. This reason, motivate us to establish the stability conditions of the Lorenz system at a point which different from the origin point and compare between them. Finally, An illustrative example shows the effectiveness and feasibility of this method.