DEPENDENCE OF STABILITY OF NICHOLSON'S BLOWFLIES EQUATION WITH MATURATION STAGE ON PARAMETERS

Jianquan Li; Baolin Zhang; Yiqun Li

doi:10.11948/2017042

2017 Volume 7 Issue 2

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Jianquan Li, Baolin Zhang, Yiqun Li. DEPENDENCE OF STABILITY OF NICHOLSON'S BLOWFLIES EQUATION WITH MATURATION STAGE ON PARAMETERS[J]. Journal of Applied Analysis & Computation, 2017, 7(2): 670-680. doi: 10.11948/2017042

Citation:

Jianquan Li, Baolin Zhang, Yiqun Li. DEPENDENCE OF STABILITY OF NICHOLSON'S BLOWFLIES EQUATION WITH MATURATION STAGE ON PARAMETERS[J]. Journal of Applied Analysis & Computation, 2017, 7(2): 670-680. doi: 10.11948/2017042

DEPENDENCE OF STABILITY OF NICHOLSON'S BLOWFLIES EQUATION WITH MATURATION STAGE ON PARAMETERS

Science College, Air Force Engineering University, 710051 Xi'an, China

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Abstract

Abstract

The stability of Nicholson's blowflies equation with maturation stage is investigated by reducing the number of parameters in the original model. We derive the condition on the stability of the positive equilibrium of the model, and discuss the dependence of the stability on the parameters by analyzing geometrically the dependence of real parts of eigenvalues of the characteristic equation with fewer parameters on the parameters. By restoring parameters, the condition on the stability of the positive equilibrium of the original model are formulated explicitly, and the corresponding regions are depicted for some different cases. The obtained result shows that the parameter determining the maximum reproductive success of the population affects only the size of the positive equilibrium, but plays no role in determining its stability.
- Nicholson's blowflies equation /
- stability /
- maturation delay /
- parameters
MSC: 34K20;92D30

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References

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