CHAPTER 11: Systems of Nonlinear Differential Equations
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In Chapter 10 we used matrix techniques to solve systems of linear first-order differential equations of the form X′ = AX + F(t). 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 valuable information about the geometric nature of solutions can be obtained by first analyzing special constant solutions called critical points and then searching for periodic solutions called limit cycles. The important concept of stability ...
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