ABSTRACT
This chapter shows that nonlinear phenomena using simple examples, tailored to throw a different light on a given differential equation. Nonlinear systems, interestingly autonomous systems themselves, can display oscillations of fixed amplitude and fixed period without any external excitation. These self-excited oscillations are called limit cycles, or self-excited oscillations. While one might think of L-C circuit, i.e., a circuit having only an inductance and a capacitance, with ideal components, for example, as a linear system exhibiting limit cycles, limit cycles in nonlinear systems are different. Chaos occurs mostly in strongly nonlinear systems. This implies that, for a given system, if the initial condition or the external input causes the system to operate in a highly nonlinear region, it increases the possibility of generating chaos. The chapter discusses other properties of first-order differential equations, mostly for differential equations, which are nonlinear.
