The following two sets of animations allow you to explore the behavior of the harvesting models in the Project from Section 7.2.
The first animation is based on Equation 1 in the Project. It displays the phase plot (in red) and the population size as a function of time (in blue) for different choices of the harvesting rate h. The initial population size is N(0)=0.5, and the black dot in the phase plot represents that long-term (stable) equilibrium population size. You can see that the long-term equilibrium population size decreases continuously as h increases, eventually resulting in extinction. The bifurcation diagram in Figure 1 of the project summarizes this behavior.
The second animation is based on Equation 2 in the Project. It again displays the phase plot (in red) and the population size as a function of time (in blue) for different choices of the harvesting rate h. The initial population size is N(0)=0.5, and the black dot in the phase plot represents that long-term (stable) equilibrium population size. Here you can see that the long-term equilibrium population size decreases continuously as h increases up to a value of h=1.125. As h increases further beyond this value the long-term equilibrium population size jumps abruptly to extinction. The bifurcation diagrams in Figures 2 and 3 of the project summarize this behavior.