lecture07

lecture07 - Phase Plane Analysis Lecture 7 Caner Kazanci...

Info iconThis preview shows pages 1–10. Sign up to view the full content.

View Full Document Right Arrow Icon
University of Georgia Lecture 7 – slide 1 Phase Plane Analysis Lecture 7 Caner Kazancı Mathematical Biology University of Georgia February 10, 2009
Background image of page 1

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

View Full DocumentRight Arrow Icon
General 2-d models University of Georgia Lecture 7 – slide 2 ˙ x = f ( x, y ) ˙ y = g ( x, y )
Background image of page 2
General 2-d models University of Georgia Lecture 7 – slide 2 ˙ x = f ( x, y ) ˙ y = g ( x, y ) Find fixed points
Background image of page 3

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

View Full DocumentRight Arrow Icon
General 2-d models University of Georgia Lecture 7 – slide 2 ˙ x = f ( x, y ) ˙ y = g ( x, y ) Find fixed points Establish stability of fixed points
Background image of page 4
General 2-d models University of Georgia Lecture 7 – slide 2 ˙ x = f ( x, y ) ˙ y = g ( x, y ) Find fixed points Establish stability of fixed points Establish the nature of the fixed points Identify the stable/unstable manifolds
Background image of page 5

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

View Full DocumentRight Arrow Icon
General 2-d models University of Georgia Lecture 7 – slide 2 ˙ x = f ( x, y ) ˙ y = g ( x, y ) Find fixed points Establish stability of fixed points Establish the nature of the fixed points Identify the stable/unstable manifolds Draw nullclines
Background image of page 6
Phase plane analysis University of Georgia Lecture 7 – slide 3 Finding fixed points: Solve ˙ x = f ( x, y ) ˙ y = g ( x, y )
Background image of page 7

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

View Full DocumentRight Arrow Icon
Phase plane analysis University of Georgia Lecture 7 – slide 3 Finding fixed points: Solve ˙ x = f ( x, y ) ˙ y = g ( x, y ) For stability: Evaluate: J = ∂f ∂x ∂f ∂y ∂g ∂x ∂g ∂y at the fixed points, and consider its eigen values.
Background image of page 8
Phase plane analysis University of Georgia Lecture 7 – slide 3 Finding fixed points: Solve ˙ x = f ( x, y ) ˙ y = g ( x, y ) For stability: Evaluate: J = ∂f ∂x ∂f ∂y ∂g ∂x ∂g ∂y at the fixed points, and consider its eigen values.
Background image of page 9

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

View Full DocumentRight Arrow Icon
Image of page 10
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 25

lecture07 - Phase Plane Analysis Lecture 7 Caner Kazanci...

This preview shows document pages 1 - 10. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online