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Advances in Continuous and Discrete Models

Theory and Modern Applications

Figure 2 | Advances in Difference Equations

Figure 2

From: Stability and Hopf bifurcation for a stage-structured predator–prey model incorporating refuge for prey and additional food for predator

Figure 2

Time series of \(u_{1}(t)\), \(u_{2}(t)\) and \(v(t)\) generated by the model (1.5): (a) Three initial values are chosen as \((u_{1}(0),u_{2}(0),v(0)) = (1.75, 2, 0.5), (2.3, 0.3, 0.1), (1.1, 1.5, 0.8)\) marked red points, blue points and black points, respectively. The dashed line stands for \(u_{2}(t) = 0\). (b) Three initial values are chosen as \((u_{1}(0),u_{2}(0),v(0)) = (14, 5.2, 0.8), (10, 2, 2.4), (9, 1.3, 0.5)\) marked red points, blue points and black points, respectively. The dashed line stands for \(u_{1}(t) = 12.444444444446397\), \(u_{2}(t) = 2.666666666667100\) and \(v(t) = 0\), respectively

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