(b) For the dynamical system dr f(x)= x - x² (1) dt sketch the function f(x) and mark the vector field direction. What are the stability properties of the fixed points. Sketch (t) as functions of t for different choices of the initial condition z(0), to illustrate these stability properties.

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Chapter2: Second-order Linear Odes
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(b) For the dynamical system
dax
f(x) = x= x²
dt
(1)
sketch the function f(x) and mark the vector field direction. What are the stability
properties of the fixed points.
Sketch (t) as functions of t for different choices of the initial condition z(0), to
illustrate these stability properties.
Transcribed Image Text:(b) For the dynamical system dax f(x) = x= x² dt (1) sketch the function f(x) and mark the vector field direction. What are the stability properties of the fixed points. Sketch (t) as functions of t for different choices of the initial condition z(0), to illustrate these stability properties.
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