文档介绍：精选优质文档-----倾情为你奉上
精选优质文档-----倾情为你奉上
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精选优质文档-----倾情为你奉上
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For the following dyn精选优质文档-----倾情为你奉上
精选优质文档-----倾情为你奉上
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精选优质文档-----倾情为你奉上
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For the following dynamical systems
1）
2）
a) Find all fixed points and classify them.
b) Sketch the phase space portrait.
Solution for 1）：
Set . Then, the equation becomes to，
Set vector variable z, we can write
, where
There is only fixed point
The Jacobian matrix
Jacobian matrix for linearized system at the fixed point,
Eigenvalues for this system are , so they have zero real part and the method of linearization cannot decide about the stability.
精选优质文档-----倾情为你奉上
精选优质文档-----倾情为你奉上
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精选优质文档-----倾情为你奉上
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Solution for 2）：
Jacobian matrix：
Jacobian matrix for linearized system at the fixed point is
Eigenvalues for this system are , repelling node, which is unstable.
精选优质文档-----倾情为你奉上
精选优质文档-----倾情为你奉上
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精选优质文档-----倾情为你奉上
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Given the system
Show that the equilibrium (0, 0) is globally asymptotically stable.
Solution：
Set . Then, the equation becomes to，
Set vector variable z, we can write
, where
There is only fixed point
The Jacobian matrix
Jacobian matrix for linearized system at the fixed point,
Eigenvalues for t