Concept explainers
Interpretation:
To explore the phase portrait of a system
Concept Introduction:
➢ For two-dimensional system, limit cycles are created or destroyed by four ways:
1) Hopf bifurcation
2) Saddle-node or fold bifurcation of cycles: In this bifurcation, two limit cycles coalesce and annihilate.
3) Infinite period bifurcation: In this bifurcation, the fixed points appear on the circle.
4) Homoclinic or saddle-loop bifurcation: In this bifurcation, the limit cycle touches the saddle point and becomes a Homoclinic orbit. This is another type of infinite-period bifurcation.
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Nonlinear Dynamics and Chaos
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