Bifurcation in a single-species Logistic model with addition Allee effect and fear effect type feedback control

In this paper, a single-species logistic model with both fear effect-type feedback control and additive Allee effect is developed and investigated using the new coronavirus as a feedback control variable. When the system introduces additive Allee effect and fear effect-type feedback control, more complicated dynamical behavior is obtained. The system can undergo transcritical bifurcation, saddle-node bifurcation, degenerate Hopf bifurcation and Bogdanov–Takens bifurcation. By numerical simulations, the system exhibits homoclinic bifurcation and saddle-node bifurcation of limit cycles as parameters are altered. Remarkably, it is the first time that two limit cycles have been discovered in a single-species logistic model with the Allee effect. Further, stronger Allee effect or stronger fear effect can lead to the extinction of the species population.