Nonlinear Dynamical Systems

This textbook provides an accessible introduction to the theory and applications of dynamical systems, with a balanced treatment of discrete-time and continuous models. Beginning with core modelling principles, the book develops the mathematical tools needed to analyse qualitative behaviour, including fixed points, stability, oscillations, and long-term dynamics. One-dimensional discrete and continuous systems are explored in detail before extending the discussion to multi-variable models, where richer behaviours emerge. Special attention is given to bifurcations and transitions between dynamical regimes, highlighting their role in parameter-dependent models. The final chapters introduce the geometric structures underlying chaotic dynamics, including fractals and strange attractors. Throughout, the emphasis is on clear exposition, intuitive reasoning, and the use of dynamical systems to understand real-world phenomena.