Absolute ultimate boundedness of genetic regulatory networks with mixed time-delays

In this paper, the absolute ultimate boundedness for genetic regulatory networks with mixed time-delays is studied. By using comparing theorem and Dini derivation method, several criteria are presented for the ultimate boundedness of GNRs. It is obtained that GRNs with mixed time-delays are absolute ultimate bounded in sense of Lagrange without any additional conditions. Finally, a simple example is given to demonstrate the correctness of the proposed results.