Interpretation:
To show that the given system is reversible, to verify that the system has three fixed points on the cylinder for
To show there is a band of closed orbits sandwiched between the circle
To sketch the phase portrait of the system on the cylinder.
To show that as
To show there are two saddles for
Concept Introduction:
A fixed point of a differential equation is a point where,
A system for which dynamics don’t change even if signs of coordinates are interchanged is called reversible system.
Phase portraits represent the trajectories of the system with respect to the parameters and give a qualitative idea about the evolution of the system, its fixed points, whether they will attract or repel the flow, etc.
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Nonlinear Dynamics and Chaos
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning