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Advances in Continuous and Discrete Models

Theory and Modern Applications

Figure 1 | Advances in Difference Equations

Figure 1

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

Figure 1

Time series of \(u_{1}(t)\), \(u_{2}(t)\) and \(v(t)\) generated by the model (1.5). Three initial values are chosen as \((u_{1}(0),u_{2}(0),v(0)) = (0.2, 0.4, 0.9), (0.6, 1.3, 1.7), (0.01, 1.5, 2.2)\) marked red points, blue points and black points, respectively. The dashed line stands for \(u_{1}(t) = 0\), \(u_{2}(t) = 0\) and \(v(t) = 0\), respectively. (a) The trivial equilibrium \(E_{0}(0,0,0)\) is unstable. (b) The trivial equilibrium \(E_{0}(0,0,0)\) is locally asymptotically stable

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