In a book on synchronization it is stated that given the ODE(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\frac{d\psi}{dt}=-\nu+\epsilon q(\psi)[/tex]

there is at least one pair of fixed points if

[tex]\epsilon q_{min}<\nu<\epsilon q_{max}[/tex]

were [tex]q_{min}, q_{max}[/tex] are the min and max values of [tex]q(\psi)[/tex] respectively.

While this could be true under particular circumstances (ie. when [tex]q_{min}<0, q_{max}>0[/tex]), I dont see how it could hold in general; such as the case when [tex]q(\psi)>0[/tex].

Can anyone shed some light on this?

Thanks in advance.

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# Fixed Points of ODE

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