Lecture Notes 19

# Lecture Notes 19 - Lecture19 Lecture 19 Application of...

This preview shows pages 1–2. Sign up to view the full content.

Lecture19 1 November 14, 2007 Outline: 1) Linear Dynamical systems du /dt=Au ; u (0)=u 0 Definitions and Interpretation General Solution and the matrix exponential e A Interpretation of General Solution as a change of Basis 2) Examples: The Romeo and Juliet Problems The Reactive Model The Contrarian Model 3) General Classification of fixed points for 2x2 systems Lecture 19: Application of Diagonalization: Linear Dynamical systems and the dynamics of love affairs Definition: an autonomous, linear dynamical system can be written as du /dt = Au u (0)=u 0 where u is a state vector, Au is a vector that describes how u changes with time and u 0 is the initial state at time t=0 Physical example: u =[ x y ]' is the position of a particle Au is the velocity of the particle u 0 =[ x0 y0]' is the initial position Linear Dynamical systems: Geometric interpretation: u (t) is a trajectory (parameterized curve) where Au is the vector tangent to the curve at any point. Linear Dynamical systems:

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

### Page1 / 5

Lecture Notes 19 - Lecture19 Lecture 19 Application of...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online