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I've been trying to figure out how to determine bifurcation values in a harmonic oscillator when either the spring constant α or damping coefficient β act as undefined parameters. I understand bifurcations in first-order DEs, but I can't figure them out in a second-order equation such as a harmonic oscillator. Could anyone give me an explanation or tip on how to achieve this?

Thanks in advance

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# Bifurcations in a harmonic oscillator equation

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