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Periodic pulse control of Hopf bifurcation in a fractional order delay predator–prey model incorporating a prey refuge

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Figure

Figure 2 Portrait of system (2.2) with initial values
Figure 4 Portrait of system (2.2) with initial values (6.46,
Figure 5 Waveform plots of system (4.24) with initial values (6.46,5.1) in Example 2. This figure illustrates thecontrol effects for the pulse width p = 10 and three different average control gain L = –0.005,–0.015,–0.045
Figure 8 Waveform plots of system (4.24) with initial values (6.46,5.1) in Example 2. This figure illustrates thecontrol effects for the pulse width p = 8 and three different control gain δ = –0.005,–0.015,–0.045

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