Introduction

In previous chapters, we studied systems that behave in a predictable and often simple way — linear systems such as simple harmonic motion or uniform acceleration. These systems are governed by equations where the variables appear to the first power, and their behavior is well understood.

However, many real-world systems are nonlinear, meaning their governing equations contain terms like:

• $x^2$, $x^3$
• $\sin x$, $\cos x$
• Products of variables

Such systems can exhibit complex and unpredictable behavior, even when governed by simple equations. This leads to the fascinating field of nonlinear dynamics and chaos.