Stability analysis of activation‐inhibition Boolean networks with stochastic function structures

Abstract

This paper analyzes the stability of activation‐inhibition Boolean networks with stochastic function structures. First, the activation‐inhibition Boolean networks with stochastic function structures are converted to the form of logical networks by the method of semitensor product of matrices. Second, based on the obtained algebraic forms, we use matrices to denote the index set of possible logical operators and transition probabilities for activation‐inhibition Boolean networks. Third, equivalence criterions are presented for the stabilities analysis of activation‐inhibition Boolean networks with stochastic function structures. Finally, an example is given to verify the validity of the results.

Event‐triggered control for sampled‐data set stabilization of switched delayed boolean control networks

“…32,33 Based on the semitensor product, an algebraic state space representation (ASSR) framework was established for the analysis and control of Boolean networks. [34][35][36][37] One can use the ASSR framework to study Boolean networks via the classic control theory. 38,39 As far as we know, there are fewer results on the event-triggered SDC for the set stabilization of SDBCNs.…”

Matrix approach to I‐detectability of partially observed discrete event systems

“…In addition, the STP approach has also been applied to other kinds of finite-value systems such as Boolean networks [24][25][26][27][28][29], game theory [30][31][32][33][34], nonlinear feedback shift register [35], and so on [36][37][38]. Please refer to previous works [39][40][41][42][43] for some comprehensive surveys of STP.…”

New Results on Controllability for a Class of Fractional Integrodifferential Dynamical Systems with Delay in Banach Spaces

“…With the rapid development of control theory, the problem of controllability for a special kind of logical control networks, Boolean control networks, was also investigated by researchers. For more details of the recent works in this regard, we refer readers to [36][37][38]. Controllability is one of the fundamental concepts in mathematical control theory.…”