### Mathematical Biosciences and Engineering

2019, Issue 5: 3215-3234. doi: 10.3934/mbe.2019160
Research article

# Bifurcation analysis of a wild and sterile mosquito model

• Received: 02 January 2019 Accepted: 31 March 2019 Published: 15 April 2019
• The bifurcation of an ordinary differential equation model describing interaction of the wild and the released sterile mosquitoes is analyzed. It is shown that the model undergoes a sequence of bifurcations including saddle-node bifurcation, supercritical Hopf bifurcation, subcritical Hopf bifurcation, homoclinic bifurcation and Bogdanov-Takens bifurcation. We also find that the model displays monostable, bistable or tristable dynamics. This analysis suggests that the densities of the initial wild mosquitoes and the released sterile ones determine the asymptotic states of both populations. This study may give an insight into the estimation number of the released sterile mosquitoes.

Citation: Xiaoli Wang, Junping Shi, Guohong Zhang. Bifurcation analysis of a wild and sterile mosquito model[J]. Mathematical Biosciences and Engineering, 2019, 16(5): 3215-3234. doi: 10.3934/mbe.2019160

### Related Papers:

• The bifurcation of an ordinary differential equation model describing interaction of the wild and the released sterile mosquitoes is analyzed. It is shown that the model undergoes a sequence of bifurcations including saddle-node bifurcation, supercritical Hopf bifurcation, subcritical Hopf bifurcation, homoclinic bifurcation and Bogdanov-Takens bifurcation. We also find that the model displays monostable, bistable or tristable dynamics. This analysis suggests that the densities of the initial wild mosquitoes and the released sterile ones determine the asymptotic states of both populations. This study may give an insight into the estimation number of the released sterile mosquitoes.

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沈阳化工大学材料科学与工程学院 沈阳 110142

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