Stability and Hopf Bifurcation in Three-Dimensional Predator-Prey Models with Allee Effect

In this study, we perform the stability and Hopf bifurcation analysis for two population modelswith Allee effect. The population models within the scope of this study are the one prey-twopredator model with Allee growth in the prey and the two prey-one predator model with Alleegrowth in the preys. Our procedure for investigating each model is as follows. First, weinvestigate the singular points where the system is stable. We provide the necessary parameterconditions for the system to be stable at the singular points. Then, we look for Hopf bifurcationat each singular point where a family of limit cycles cycle or oscillate. We provide the parameterconditions for Hopf bifurcation to occur. We apply the algebraic invariants method to fullyexamine the system. We investigate the algebraic properties of the system by finding allalgebraic invariants of degree two and three. We give the conditions for the system to have afirst integral.