Global dynamics of neoclassical growth model with multiple pairs of variable delays

Taking into account the effects of multiple pairs of variable delays, this paper deals with the global dynamics for a class of differential neoclassical growth models. We aim to obtain significant insights into better understanding of how the multiple pairs of variable delays essentially affect the stability and attractiveness of the unique positive equilibrium point. First of all, we prove that every solution of the IVP (initial value problem) with respect to the addressed system exists globally and is positive and bounded above. Secondly, with the help of the methods of fluctuation lemma and analytical techniques, two delay-independent criteria and one delay-dependent criterion on the attractivity of the unique positive equilibrium point are established, which improve and complement some published results. Lastly, two examples with the numerical simulation are arranged to illustrate the effectiveness and feasibility of the obtained theoretical results.