Non-linear Dynamics

Recommended

Percival, I.; Richards, D. Introduction to Dynamics; Cambridge University Press: Cambridge ; New York, 1982.

Excellent!

Rand, R. H. (2005) Lecture Notes on Nonlinear Vibrations. PDF

As a summary, this is an excellent resource; and it's freely available from the author!

Colombo, A. Nonlinear Dynamics, 2025. PDF.

Mathematical and a bit terse, but it defines all new technical terms. (If you think that should always be the case: Welcome to academia.)

Strogatz, S. H. (2015). Nonlinear dynamics and chaos: With applications to physics, biology, chemistry, and engineering (Second edition). Westview Press.

Krishnaswami, G. S. (2020). Notes on Nonlinear Dynamics. PDF

Concise.

Ross, S. L. (2004). Differential equations (Third edition, Wiley student edition). Wiley India.

The chapter on nonlinear differential equations is especially neat. I liked the idea of introducing critical points and paths first for linear systems, and then for nonlinear systems.