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Advances in Continuous and Discrete Models

Theory and Modern Applications

Figure 5 | Advances in Difference Equations

Figure 5

From: Analysis of a stochastic ratio-dependent one-predator and two-mutualistic-preys model with Markovian switching and Holling type III functional response

Figure 5

Trajectory and frequency of the discrete Markov chain. Subgraphs (a) and (b) denote the trajectory and frequency of the discrete Markov chain \(r_{n}\) taking value in \(\{1,2,3\} \), respectively. \(r_{n}=1\), \(r_{n}=2\) and \(r_{n}=3\) mean that the overall system (1.3) switches to subsystem (6.3), (6.4) and (6.5) in step n, respectively. The change of \(r_{n}\) in (a) means the process of regime switching of system (1.3) among subsystems (6.3), (6.4) and (6.5). The frequency of \(r_{n}\) in (b) shows the result of regime switching-the total number of steps of the overall system (1.3) switching to (6.3), (6.4) and (6.5). This graph shows that under the control of the Markov chain, the overall system (1.3) mostly switches to subsystem (6.5) in Case 6.2.1.

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