A note on monostability and bistability of boolean networks based on structure graphs

This paper addresses monostability and bistability of Boolean networks which described by the network structure and the component dynamics based on structure graphs. First of all, this paper is unfolded with the identification the unstable Boolean network in accordance with a particular property of structure graphs. Provided this property could be satisfied, then any component dynamics cannot make this network monostable or bistable. Subsequently, the paper proposes a specific condition based on structure graphs. If this condition could be satisfied, then at least one component dynamics can make corresponding Boolean network monostable or bistable. The above-mentioned property and condition of judging the stability of Boolean networks are very useful for studying the properties of component dynamics units of Boolean networks. Finally, several examples are presented to verify our conclusions.