11.1 Autonomous Systems

11.2 Stability of Linear Systems

11.3 Linearization and Local Stability

11.4 Autonomous Systems as Mathematical Models

11.5 Periodic Solutions, Limit Cycles, and Global Stability

Chapter 11 in Review

In Chapter 10 we used matrix techniques to solve systems of linear first-order differential equations. When a system of differential equations is not linear, it is usually not possible to find solutions that can be expressed in terms of elementary functions. In this chapter we will see that information on the geometric nature of the solutions can be acquired by first analyzing special constant solutions of the system and then searching for periodic solutions. The concept of stability will be introduced and illustrated with mathematical models from physics and ecology.