12 · Local Nonlinear Dynamics
Differential Equations
Local Rules, States, and Models
1 · What is a Differential Equation
2 · Finding Solutions
3 · A Glimpse of the Theory
4 · Building and Exploring Models
Linear Equations and Flows
5 · Equations and Solution Spaces
6 · Linear Evolution
7 · The Matrix Exponential
8 · The Geometry of Linear Flows
9 · Modes of Linear Systems
10 · Forcing and Linear Response
Low-Dimensional Nonlinear Dynamics
11 · Beyond Linear Flows
12 · Local Nonlinear Dynamics
13 · Cycles in the Plane
14 · Bifurcations of Equilibria
15 · Bifurcations of Oscillations
Appendices
A · Calculus Review
B · Linear Algebra Review
Differential Equations
Local Rules, States, and Models
1 · What is a Differential Equation
2 · Finding Solutions
3 · A Glimpse of the Theory
4 · Building and Exploring Models
Linear Equations and Flows
5 · Equations and Solution Spaces
6 · Linear Evolution
7 · The Matrix Exponential
8 · The Geometry of Linear Flows
9 · Modes of Linear Systems
10 · Forcing and Linear Response
Low-Dimensional Nonlinear Dynamics
11 · Beyond Linear Flows
12 · Local Nonlinear Dynamics
13 · Cycles in the Plane
14 · Bifurcations of Equilibria
15 · Bifurcations of Oscillations
Appendices
A · Calculus Review
B · Linear Algebra Review
Chapter 12
Local Nonlinear Dynamics