Dynamics of a discrete-time host–parasitoid system with cannibalism

Figures & data

Figure 1. This figure provides simulation results for system (1) with function g given in Equation (26) and parameter values given in Equation (27): (a) plots y=det(J(E ₁)) against c; (b) provides a closed invariant curve solution when c=1.079; (c) is the bifurcation diagram with c as the bifurcation parameter; and (d) plots a particular solution when c=2.0, x ₁(0)=2.0 and x ₂(0)=3.0, where ‘.’ denotes x ₁ and ‘-’ denotes x ₂.

Figure 2. This figure provides simulation results for system (17) with function g given in Equation (26), f given in Equation (28), and parameter values given in Equation (29): (a) provides the time evolution of a particular solution when c=β=1.0; (b) presents the time evolution of a particular solution when c=1.0 and β=2.0; (c) plots the time evolution of a particular solution when c=2.0 and β=1.0; (d) provides a particular solution when c=2.0 and β=3.0. In all these plots, ‘.’ denotes x ₁ and ‘*’ denotes p and initial conditions are (1, 1, 2) for each solution presented.