Stability of Lorenz System at the Second Equilibria Point based on Gardano^s Method
S. F. AL-Azzawi1,*, Mujiarto2 , L. Patria3 , A. Sambas2 and W. S. M. Sanjaya4

1 Department of Mathematics, College of Computer Sciences and Mathematics,
University of Mosul, Mosul, Iraq
2 Department of Mechanical Engineering, Universitas Muhammadiyah Tasikmalaya, Indonesia
3 Department of Information Systems, Universitas Terbuka, Indonesia
4 Department of Physics, Universitas Islam Negeri Sunan Gunung Djati, Bandung, Indonesia

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.

Keywords: Lorenz system, Gardanos method

Topic: Engineering and Technology