Overview
Description
Motion of systems governed by ordinary differential equations: phase portraits, point attractors, limit cycles, stability, bifurcations, Poincaré sections, chaos & strange attractors, Lyapunov exponents, fractal dimensions, delay coordinates. Forced, nonlinear oscillations: jump phenomena, parametric & harmonic resonances, perturbation methods including averaging & multiple-scales analysis. Systems governed by discrete maps: return maps, cobweb plots, period-doubling bifurcations, intermittency.
Units
Lecture3
Catalog Details
Offering
Offered: Every Spring
Terms
spring
Attributes
Standard
Learning Outcomes
- acquire and apply new knowledge as needed, using appropriate learning strategies.
- solve low-order nonlinear equations algebraically or numerically.