Exercise Notes for the Course Nonlinear Dynamical Models
Content
Introduction
1. The Classification of Linear Oscillators
1.1 Linear Focus Attractor
1.2. Linear Focus Attractor in Python
2. The Mathematical Pendulum - The System of Separatrices
3. The Saddle-Point and the Pitchfork Bifurcations
3.1. The Saddle-Point Bifurcation
3.2. The Pitchfork Bifurcation
4. The Duffing’s Equation
5. Limit Cycles. The van der Pol Oscillator
6. The Birth and the Destruction of Limit Cycles. The Hopf Bifurcation
7. Homoclinic and Heteroclinic Bifurcations
8. The Forced Mathematical Pendulum. The Road to Chaos
Concluding Remarks and Further Information
References