Theory and Modern Applications
Table 1 Stability of trivial equilibrium point \(E_{0}\)
From: Stability and bifurcation analysis for a single-species discrete model with stage structure
Conditions | Distribution of roots of Eq. (6) | Topological types of \(E_{0}\) |
|---|---|---|
bδ<(1 − α)(1 − β) | \(-1<\lambda_{2}<\lambda_{1}<1\) | sink, stable |
bδ = (1 − α)(1 − β) | \(-1<\lambda_{2}=\alpha+\beta-1<\lambda _{1}=1\) | non-hyperbolic, stable |
(1 − α)(1 − β)<bδ<(1 + α)(1 + β) | \(-1<\lambda_{2}<1<\lambda_{1}\) | saddle, unstable |
bδ = (1 + α)(1 + β) | \(-1=\lambda_{2}<1<\lambda_{1}=\alpha+\beta+1\) | non-hyperbolic, unstable |
bδ>(1 + α)(1 + β) | \(\lambda_{2}<-1<1<\lambda_{1}\) | source, unstable |