Periodic attractors for the varactor equation
نویسندگان
چکیده
We consider a class of differential equations, ẍ + γẋ + x = f(ωt), with p ∈ N and ω ∈ R, describing one-dimensional dissipative systems subject to a periodic forcing. For p = 1 the equation describes a resistor-inductor-varactor circuit, hence the name ‘varactor equation’. We concentrate on the limit cycle described by the trajectory with the same period as the forcing; numerically, for γ large enough, it appears to attract all trajectories which remain bounded in phase space. We find estimates for the basin of attraction of this limit cycle, which are good for large values of γ. Also, we show that the results extend to the case of quasi-periodic forcing, provided the frequency vector ω satisfies a Diophantine condition — for instance, the Bryuno or the standard Diophantine condition.
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