Concept explainers
Interpretation:
Find the fixed points and classify them, sketch the neighboring trajectories
Concept Introduction:
The parametric curves traced by solutions of a differential equation are known as trajectories.
The geometrical representation of a collection of trajectories in a phase plane is called a phase portrait.
The point which satisfies the condition
Closed Orbit corresponds to the periodic solution of the system i.e.
If nearby trajectories moving away from the fixed point then the point is said to be saddle point.
If the trajectories swirling around the fixed point then it is an unstable fixed point.
If nearby trajectories moving towards the fixed point then the point is said to be a stable fixed point.
To check the stability of fixed-point, use the Jacobian matrix:
The point
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Check out a sample textbook solutionChapter 6 Solutions
Nonlinear Dynamics and Chaos
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