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Chapter Review Sheets for
Elementary Differential Equations and Boundary Value Problems, 8e
Chapter
9: Nonlinear Differential Equations and Stability
Definitions:
•
Equilibrium Solutions
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Critical Points
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Trajectory
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Phase P1ane,
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Phase Portrait
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Node; Nodal Sink, Nodal Source, Saddle Point, Proper Node, (Star Point)
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Improper Node, (Degenerate Node), Spiral Sink, Spiral Source, Autonomous
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Stable, Unstable Isolated Critical Point, Almost Linear System,
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Basis of attraction
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Globally asymptotically stable
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Region of Asymptotic Stability, Nullclines
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Separatrix
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Liapunov's Method
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Positive Definite, Negative Definite, Positive Semidefinite, Negative Semidefinite
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Limit Cycle
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Asymptotically Stable
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Strange attractors
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Chaotic system/equation
Theorems:
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Theorem 9.3.1:
Stability of critical points of linear systems dependence on eigenvalues.
•
Theorem 9.3.2:
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 Spring '10
 DorothyWallace
 Differential Equations, Equations, Critical Point

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