lecture07

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

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University of Georgia Lecture 7 – slide 1 Phase Plane Analysis Lecture 7 Caner Kazancı Mathematical Biology University of Georgia February 10, 2009

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General 2-d models University of Georgia Lecture 7 – slide 2 ˙ x = f ( x, y ) ˙ y = g ( x, y )
General 2-d models University of Georgia Lecture 7 – slide 2 ˙ x = f ( x, y ) ˙ y = g ( x, y ) Find fixed points

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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
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

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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
Phase plane analysis University of Georgia Lecture 7 – slide 3 Finding fixed points: Solve ˙ x = f ( x, y ) ˙ y = g ( x, y )

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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.
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.

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## This note was uploaded on 07/08/2011 for the course BM 501 taught by Professor Kop during the Spring '11 term at Bloomsburg.

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

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