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 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.
To find the fixed point of the system put
To check the stability of fixed-point use Jacobian matrix
The point
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Check out a sample textbook solutionChapter 6 Solutions
Nonlinear Dynamics and Chaos
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageAlgebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal Littell