This lesson covers the concept of bifurcation in non-linear vibration. It delves into the different types of bifurcation, including saddle node, pitchfork, and trans-critical bifurcation. The lesson also explains how to identify these bifurcations using eigenvalues and Jacobian matrices. It further discusses the stability of systems and how it changes at bifurcation points. For instance, it explains how a stable trivial state can transition to a stable non-trivial state in a supercritical pitchfork bifurcation. The lesson also touches on the concept of basin of attraction and the use of harmonic balance method in solving equations.

- Bifurcation in non-linear vibration refers to a qualitative or quantitative change in the system's response at a critical point.
- There are different types of bifurcation, including saddle node, pitchfork, and trans-critical bifurcation.
- Eigenvalues and Jacobian matrices are essential tools in analyzing bifurcation.
- The stability of a system can change at bifurcation points, transitioning from a stable state to an unstable state or vice versa.
- The basin of attraction can be used to determine the stability of different solutions in a system.
- The harmonic balance method can be used to solve equations in non-linear vibration analysis.

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