Complexity and Chaos in Dynamical Systems

Lecturer: Yulia Timofeeva (Office: D2.12, Centre for Complexity Science, Zeeman building)

Lecture Notes

• Introduction, first-order systems (including flows on the circle)

Fireflies (paper of Ermentrout & Rinzel)

• Second and higher order systems (linear and nonlinear)
• Nonlinear oscillations1 (Poincare-Bendixson theorem, relaxation oscillators)
• Nonlinear oscillations2 (perturbation theory, coupled oscillators, Poincare map)
• Introduction to Chaos (Lorenz equations)
• 1D maps
• Routes to chaos. Fractals. Global bifurcations

Exam questions

Assignments

• Assignment 1

Assignment 1 is due on Thursday, 26 November at 10am

• Assignment 2

Assignment 2 is due on Tuesday, 8 December at 5pm

XPPAUT models

• linear2d.ode
• cusp.ode
• SN.ode
• phase.ode
• Hodgkin-Huxley.ode
• Morris-Lecar1.ode
• Morris-Lecar2.ode (different parameters)

XPPAUT

XPPAUT - a tool for simulating, animating and analysing dynamical systems

Version for Windows

B. Ermentrout (2002) "Simulating, Analyzing, and Animating Dynamical Systems (A guide to XPPAUT for researchers and students)" (SIAM)

Examples from the book (.ode files)