One-Bit Function Perturbation Impact on Robust Set Stability of Boolean Networks with Disturbances

Abstract

This paper investigates the one-bit function perturbation (OBFP) impact on the robust set stability of Boolean networks with disturbances (DBNs). Firstly, the dynamics of these networks are converted into the algebraic forms utilizing the semi-tensor product (STP) method. Secondly, OBFP’s impact on the robust set stability of DBNs is divided into two situations. Then, by constructing a state set and defining an index vector, several necessary and sufficient conditions to guarantee that a DBN under OBFP can stay robust set stable unchanged are provided. Finally, a biological example is proposed to demonstrate the effectiveness of the obtained theoretical results.

Keywords

• boolean networks
• disturbances
• one-bit function perturbation
• robust set stability
• semi-tensor product of matrices