Dynamic System Analysis of Investment in Both Production and R&D with Time Delay

This paper, according to the process of capital return, establishes a differential dynamics model investment with two time delays. When both delays are zero, it is proved that positively invariant, uniformly bounded, and globally asymptotically stable by using comparison principle Bendixson–Dulac theorem. at least one delay not Hopf bifurcation theorem, conditions local asymptotic stability existence periodic solution obtained. By normal form theory center manifold theory, discriminant formula property given. Under condition controlled delay, numerically simulated verify correctness relevant analytical conclusions. Therefore, describes dynamic development trend project quite closely.