LIFESCI 30B Study Guide - Midterm Guide: Hopf Bifurcation, Limit Cycle, Attractor
Document Summary
Lectures 1-8 textbook 4. 1, 4. 2, 4. 3, 5. 1, 5. 2, 6. 1, 6. 2. Section 4. 1; section 4. 2; from section 4. 3, the subsections stable oscillations in an ecological model and hopf bifurcation and the causes of oscillation . Lecture 1. 1: the concept of an attractor in the state space of a model. Attractor is a set that pulls trajectories towards it. Definition- an attractor of m is a set a in um such that any point x(t0) close enough to a will flow towards. An attractor can be any set in the state space um: point attractor and limit cycle attractor (lca) Point attractors: the set a is a single point in the line (namely, a stable equilibrium point) Limit cycle attractor: the set a is a closed loop in xm (the closed loop diagram: oscillation is represented by a closed loop trajectory in the state space.
