UCSC: Math 145, Introduction to Chaos Theory, Spring 2017

Part I: Iterated Maps

Week 01, 1D iterations
Tuesday 4/04, sensitivity, bifurcations
Thursday 4/06, applications
Week 02, 2D iterations
Tuesday 4/11, critical curves, mira, dorband
Thursday 4/13, applications

Part II: Flows

Week 03, 1D flows, 2D Flows
Tuesday 4/18, 1D flows, gradient flows, catastrophe theory the fold bifurcation
Thursday 4/20, 2D flows, attractors and basins, the fold, the Hopf bifurcaton
Week 04, 3D flows, chaos
Tuesday 4/25, 3D flows, forced pendula and oscillators
Thursday 4/27, 3D flows, the classical chaotic attractors
Week 05, 3D flows, stability, horseshoes
Tuesday 5/02, 3D flows, global behavior (Chs. 10, 11, 12)
Thursday 5/04, 3D flows, global behavior (Chs. 13, 14, 15)
Week 06, 3D flows, bifurcations
Tuesday 5/09, Applications: cybernetics, neuron models, synchronization
Thursday 5/11, Applications: neural networks, economic networks

Part III: Complex Systems

Week 07, System dynamics, guest presentation (David Dunn and David Kant)
Tuesday 5/16, System dynamics
Week 08, Complex systems, definitions
Tuesday 5/23, Complex dynamical systems
Thursday 5/25, Formal definitions
Week 09, Definitions
Tuesday 5/30, Formal definitions, cont'd
Week 10, Economics and Neurophysiology applications updated
Tuesday 6/6, Business cycles
Thursday 6/8, Chaos in the brain
FINAL: Tuesday 6/13, 4-7 pm
Revised 09 June 2017 by Ralph