Nonlinear systems are ubiquitous in real world. In this case the superposition principle is no more valid meaning that the response of the system is not proportional to the input it receives; the sum of different solutions is not a solution anymore. After a brief introduction, we study  systems with increasing complexity starting from one dimensional systems to multiple dimension ones. As nonlinear equations are difficult to solve, nonlinear systems are commonly approximated by linear equations using linearization about a basic state. Multiple solutions can exist that are visited through bifurcations when a parameter of the system is varied and can lead to interesting phenomena such as chaos.

• Nonlinear dynamics and chaos, S. Strogatz, Westview Press.
• Structures dissipatives, chaos et turbulence, P. Manneville, Aléa Saclay.
• Course Notes for Nonlinear Dynamics, L. Tuckerman, https://www.pmmh.espci.fr/~laurette/explanatory