Syllabus

Flows on the line: Introduction; Fixed points and stability; Population growth; Linear Stability Analysis; Existence and Uniqueness; Impossibility of oscillations; Potentials

Bifurcations: Saddle-node bifurcation; Transcritical bifurcation; Laser threshold; Pitchfork bifurcation; Overdamped bead on a rotating hoop; Imperfect bifurcations and catastrophes; Insect outbreak

Flows on a circle: Examples and Definitions; Uniform Oscillator; Nonuniform Oscillator; Overdamped Pendulum; Fireflies; Superconducting Josephson junctions

Linear Systems: Definitions and examples; Classification of linear systems; Love Affairs

Phase Plane: Phase portraits; Existence, uniqueness and topological consequences; Fixed points and linearization; Rabbits versus sheep; Conservative systems; Reversible systems; Pendulum

Limit Cycles: Examples; Ruling out closed orbits; Poincare-Bendixson theorem; Lienard systems

Bifurcations Revisited: Saddle-node, transcritical and pitchfork bifurcaations; Hopf bifurcations; Oscillating chemical reactions; Global bifurcations of cycles; Hysterisis in the driven pendulum and Josephson junction; Coupled oscillators and quasiperiodicity; Poincare maps

Lorenz equations: A chaotic waterwheel; Simple properties of the Lorenz equations; Chaos on a strange attractor; Lorenz map; Exploring parameter space

One-dimensional maps: Fixed points and cobwebs; Logistic map: Numerics and Analysis; Periodic windows;

Liapunov exponent; Universality and experiments

Fractals: Countable and Uncountable Sets; Cantor set; Dimension of self-similar fractals; Box dimension; Pointwise and correlation dimensions

Strange attractors: Examples; Henon map; Rossler system; Chemical chaos