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

Article

DOI: 10.1007/s10884-015-9432-3

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

## Abstract

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.

### Keywords

Logistic modelInstantaneous and delayed density dependenceStability switchesHopf bifurcation

### Mathematics Subject Classification

34K0834K1834K2035R1092E20
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