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Journal of Biological Dynamics Volume 8, 2014 - Issue 1
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Original Articles

Bifurcations and dynamics of a discrete predator–prey system

Rasoul AsheghiDepartment of Mathematical Sciences, Isfahan University of Technology, Isfahan84156, IranCorrespondence[email protected]
Pages 161-186 | Received 16 Nov 2013, Accepted 18 May 2014, Published online: 17 Jun 2014

Figures & data

Figure 1. Graph of the functions f1 and f2 in the case 0<a≤1/k.

Figure 1. Graph of the functions f1 and f2 in the case 0<a≤1/k.

Figure 2. Graph of the functions f1 and f2 in the case a>1/k.

Figure 2. Graph of the functions f1 and f2 in the case a>1/k.

Figure 3. Graph of the functions g1 and g2 in the case k>1.

Figure 3. Graph of the functions g1 and g2 in the case k>1.

Figure 4. Position of Ŷ3(k) for k∈(⅓, 1].

Figure 4. Position of Ŷ3(k) for k∈(⅓, 1].

Figure 5. Shape of Ω in the case k>1.

Figure 5. Shape of Ω in the case k>1.

Figure 6. Graph of the functions g1 and g2 in the case 0<k≤1.

Figure 6. Graph of the functions g1 and g2 in the case 0<k≤1.

Figure 7. Shape of Ω in the case 0<k≤1.

Figure 7. Shape of Ω in the case 0<k≤1.

Figure 8. Phase diagram when r=3.7, a=10, k=0.5, (x0, y0)=(0.3, 0.3) and n=25, 000.

Figure 8. Phase diagram when r=3.7, a=10, k=0.5, (x0, y0)=(0.3, 0.3) and n=25, 000.

Figure 9. Phase diagram when r=3.6, a=10, k=0.5, (x0, y0)=(0.3, 0.3) and n=25, 000.

Figure 9. Phase diagram when r=3.6, a=10, k=0.5, (x0, y0)=(0.3, 0.3) and n=25, 000.

Figure 10. Phase diagram when r=1.6, a=27, k=2, (x0, y0)=(0.6, 0.6) and n=25, 000.

Figure 10. Phase diagram when r=1.6, a=27, k=2, (x0, y0)=(0.6, 0.6) and n=25, 000.

Figure 11. Phase diagram when r=1.49, a=27, k=2, (x0, y0)=(0.6, 0.6) and n=25, 000.

Figure 11. Phase diagram when r=1.49, a=27, k=2, (x0, y0)=(0.6, 0.6) and n=25, 000.

Figure 12. Phase diagram when r=2.2, a=50, k=0.9, (x0, y0)=(0.5, 0.5) and n=25, 000.

Figure 12. Phase diagram when r=2.2, a=50, k=0.9, (x0, y0)=(0.5, 0.5) and n=25, 000.

Figure 13. Phase diagram when r=2.0, a=50, k=0.9, (x0, y0)=(0.5, 0.5) and n=25, 000.

Figure 13. Phase diagram when r=2.0, a=50, k=0.9, (x0, y0)=(0.5, 0.5) and n=25, 000.

Table 1.  The numerical exact values for the positive fixed point (x*, y*) and for the coefficient a(0) corresponding to the chosen values of the parameters (a, k).

Table 2.  The numerical exact values for (r1, λ2, F) corresponding to the chosen parameter values for (a, k).

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