Journal of Dynamics and Differential Equations

, Volume 29, Issue 1, pp 113–130

Stability Switches in a Logistic Population Model with Mixed Instantaneous and Delayed Density Dependence


DOI: 10.1007/s10884-015-9432-3

Cite this article as:
Yan, X. & Shi, J. J Dyn Diff Equat (2017) 29: 113. doi:10.1007/s10884-015-9432-3


The local asymptotic stability and stability switches of the positive equilibrium in a logistic population model with mixed instantaneous and delayed density dependence is analyzed. It is shown that when the delayed dependence is more dominant, either the positive equilibrium becomes unstable for all large delay values, or the stability of equilibrium switches back and force several times as the delay value increases. Compared with the logistic model with the instantaneous term and a delayed term, our finding here is that the incorporation of another delayed term can lead to the occurrence of multiple stability switches.


Logistic model Instantaneous and delayed density dependence Stability switches Hopf bifurcation 

Mathematics Subject Classification

34K08 34K18 34K20 35R10 92E20 

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of MathematicsLanzhou Jiaotong UniversityLanzhouChina
  2. 2.Department of MathematicsCollege of William and MaryWilliamsburgUSA

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