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Stability and Hopf Bifurcation Analysis of a Fractional-Order Nicholson Equation with Two Different Delays |
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PP: 201-215 |
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doi:10.18576/amis/180120
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Author(s) |
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H. A. A. El-Saka,
D. El. A. El-Sherbeny,
A. M. A. El-Sayed,
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Abstract |
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| In this paper, we investigate the stability and Hopf bifurcation of fractional-order Nicholson equation with two different delays r1,r2 > 0: Dαy(t) = −μy(t −r1)+ρy(t −r2)e−γy(t−r2), t > 0. We obtain stability regions by analyzing the characteristic equation of the linearized model around the equilibrium points. We evaluate the effects of ρ and μ on the equilibrium point, which influence the model’s stability and Hopf bifurcation. By choosing μ, ρ, fractional order α and time delays as a bifurcation parameters, the delay bifurcation curve for the emergence of the Hopf bifurcation is determined. Finally, numerical simulations are presented to illustrate the efficiency and validity of our results.
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