Figure 2
From: Non-linear population discrete models with two time scales: re-scaling of part of the slow process
Comparison between the complete and the reduced systems. Total population corresponding to certain initial conditions for system (18) and for system (16) for three different values of k, i.e., \(k\in \{1,5,10\}\). The simulations have been run until time \(t=10^{4}\) and only the last 6 times are shown. Parameter values: \(s_{1}^{1}=0.3\), \(s_{2}^{1}=0.47\), \(s_{3}^{1}=0.7\), \(s_{1}^{2}=s_{2}^{2}=s_{3}^{2}=0.5\), \(\phi ^{1}=3.8\), \(\phi ^{2}=3.5\), \(c_{1}=c_{2}=1\), \(d_{1}=5.3\), \(d_{2}=5.6\), \(v_{1}^{1}=0.3\), \(v_{2}^{1}=0.25\), \(v_{3}^{1}=0.1\). Initial condition: \(X(0)=(0.02,0.02,0.05,0.05,0.02,0.02)\)