Periodic oscillation in delayed gene networks with SUM regulatory logic and small perturbations

In this paper, we derive new criteria for evaluating the global stability of periodic oscillation in delayed gene networks with SUM regulatory logic and small perturbation, which appear in many biological systems at biomolecular or cellular levels due to the weak coupling and signal diffusion (or transport) process. Our results rely on the Lipschtiz conditions of Hill function, topology of gene networks and delay kernels. In particular, Our method based on the proposed model transforms the original network into matrix analysis problem, thereby not only significantly reducing the computational complexity but also making analysis of periodic oscillation tractable for even large-scale nonlinear networks.