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Example sentences for: hopf

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Whenever a stable periodic solution loses stability as we vary the underlying parameters of the system and this solution transitions to another qualitative solution - for example, a steady-state equilibrium - we say that the system undergoes a Hopf bifurcation.
These diagrams illustrate that Hopf bifurcations occur for each parameter; that is, the oscillatory behaviour exists only in a limited range of parameters around the nominal value.
Suppose that Hopf bifurcations occur at
The particular parameters were either increased or decreased so as to bring them closer to the Hopf bifurcation.