Bifurcation analysis in single-species population model with delay
The authors consider the scalar differential-delay equation \[ {dN(t)\over dt}= be^{-aN(t-\tau)}N(t-\tau) e^{-d_1\tau}- dN(t) \] under the conditions \(a> 0\), \(d>0\), \(d_1\geq 0\), \(b> de^{d_1\tau+ 2}\), \(\tau\geq 0\). They study the stability of the positive equilibrium \(N= N^4= {1\over a}\ln{b\over de^{d_1\tau}}\) and prove the occurrence of Hopf bifurcation with \(\tau\) as bifurcation parameter. The direction of Hopf bifurcation is also determined.
scientific article; zbMATH DE number 5774152
scientific article