This paper is devoted to the existence and bifurcations of positive periodic solutions of nonlinear differential equation related to the Liebau phenomenon in rigid pipe-tank flow configuration. We obtain some more general requirements on the existence of a positive harmonic solution which improves the results in literatures. It is revealed that the system undergoes saddle node bifurcation, period doubling bifurcation and Neimark-Sacker bifurcation generating various periodic solution of different stability types. The multiplicity of both the positive harmonic solution and positive 2-th order subharmonic solution is first detected in this equation by numerical bifurcation analysis. Moreover, this work reveals that the positive subharmonic solutions of the nonlinear differential equation will also lead to the Liebau phenomenon in the model, which will shed some new insights for future research.
MSC—34B16; 34C25; 37G15.