Transcritical bifurcation and Neimark-Sacker bifurcation of a discrete predator-prey model with herd behaviour and square root functional response

Figures & data

Figure 1. Bifurcation of the system (7) in $(b,x)$-plane and maximal lyapunov exponents.

Figure 2. Phase portraits for the system (7) with $\mathrm{a}=0.05$, $\mathrm{d}=0.55$ and different $b$ with the initial value $(x_0,y_0)=(0.44,4.5)$ outside the closed orbit.

Figure 3. Phase portraits for the system (7) with $\mathrm{a}=0.05$, $\mathrm{d}=0.55$ and different $b$ with the initial value $(x_0,y_0)=(0.44,7.47)$ inside the closed orbit.

Figure 4. Phase portraits for the system (7) with $\mathrm{a}=0.05$, $\mathrm{d}=1.5$ and different $b$ with the initial value $(x_0,y_0)=(0.46,6.5)$.