Global behaviour of a predator–prey like model with piecewise constant arguments

Figures & data

Figure 1. Graph of the iteration solution of $M\left(n\right)$, $N\left(n\right)$ and $Z\left(n\right)$,where $\alpha =1.24379\times {10}^{-7}$.

Figure 2. Graph of the iteration solution of $M\left(n\right)$, $N\left(n\right)$ and $Z\left(n\right)$, where $\alpha =1.24379\times {10}^{-7}$. Parameter values are taken Example 2.3.

Figure 3. Graph of the $(\beta ,\mid \lambda \mid )$. Parameter set is taken from Example 2.3.

Figure 4. Graph of Neimark-Sacker bifurcation of system (7(7) $\begin{array}{rl}M(n+1)& =\frac{M\left(n\right)(r_1-{\alpha }_{1}N(n\left)\right)}{r_1{K}_{1}M\left(n\right)+(r_1-{\alpha }_{1}N(n)-r_1{K}_{1}M(n\left)\right)\exp (-(r_1-{\alpha }_{1}N\left(n\right)\left)\right)},\\ N(n+1)& =N\left(n\right)\exp \left(\beta Z\right(n)-d_1-{\alpha }_{2}M(n\left)\right),\\ Z(n+1)& =\frac{Z\left(n\right)(r_2-\beta N(n\left)\right)}{r_2{K}_{2}Z\left(n\right)+(r_2-\beta N(n)-r_2{K}_{2}Z(n\left)\right)\exp (-(r_2-\beta N\left(n\right)\left)\right)},\end{array}$(7) ) for $\beta =7.95907\times {10}^{-8}$, where $M\left(0\right)=1\times {10}^6$, $N\left(0\right)=1.5\times {10}^5$, $Z\left(0\right)=9\times {10}^5$. The other parameters are taken Example 2.3.

Figure 5. Graph of iteration solution of the system for $\beta =2\times {10}^{-8}$. The other parameters and initial conditions are the same as Figure 4.

Figure 6. Graph of iteration solution of the system for $\beta =1.5\times {10}^{-7}$. The other parameters and initial conditions are the same as Figure 4.

Figure 7. Graph of the iteration solution of $M\left(n\right)$, $N\left(n\right)$ and $Z\left(n\right)$, where $\alpha =2.74379\times {10}^{-6}$. The other parameters are the same as Figure 6.