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Suppose that a two-dimensional system dY/dt = F(Y) has

Chapter , Problem 9

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QUESTION:

Suppose that a two-dimensional system dY/dt = F(Y) has exactly one equilibrium point and that point is a source. Describe two different possible long-term behaviors for a solution with an initial condition that is near the equilibrium point.

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QUESTION:

Suppose that a two-dimensional system dY/dt = F(Y) has exactly one equilibrium point and that point is a source. Describe two different possible long-term behaviors for a solution with an initial condition that is near the equilibrium point.

ANSWER:

Step 1 of 2

Suppose equilibrium point be  and the initial point be  .

Determine the long term behaviour of the solution as follows:

When  then it gives:

 as

And  as

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