Geometric stability switch criteria in delay differential equations with two delays and delay dependent parameters
In considering stability of delay differential equations with two delays at an equilibrium point, the characteristic equation of the linearised delay differential equation may have the form \[P_0(\lambda, \tau) + P_1(\lambda, \tau)e^{-\lambda\tau} +P_2(\lambda, \tau)e^{-\lambda\tau_1} =0,\] where $\tau\in I \subset\mathbb{R}_+, \tau_1\in\mathbb{R}_+, P_{\ell}(\lambda, \tau), \ell = 0, 1, 2$, are polynomials in $\lambda$. In this paper, crossing curves on the $(\tau, \tau_1)$-plane on which the characteristic equation has pure imaginary roots are investigated under certain assumptions. Based on these crossing curves, stability switch can be obtained for the delay parameters $\tau$ and $\tau_1$. Although results on stability switch for equations with one delay $\tau$ can be found in literature, the authors claim that the investigation on stability switch for equations with two delays is new. As an example, stability switch analysis is provided for an epidemic model with two delays.
scientific article; zbMATH DE number 7040850
scientific article