The exponential convergence for a delay differential neoclassical growth model with variable delay

The paper investigates the delay differential neoclassical growth model x′(t)=βxγ(t-τ(t))e-δx(t-τ(t))-αx(t)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x'(t)=\beta x^\gamma (t-\tau (t))e^{-\delta x(t-\tau (t))}-\alpha x(t)$$\end{document} with γ>1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma >1$$\end{document} and variable delay. We discuss the existence and positivity of solutions and discover the exponential convergence of positive equilibriums. Moreover, we give several examples with numerical simulations to demonstrate theoretical results.