Set Stability Analysis Of Logical Dynamic System And Its Application In Evolutionary Game

With the rapid development of systems biology,logical dynamic system,a dynamic model based on multi-valued logical control network(including Boolean network)for biological systems,has become a research hot-spot in the control field.However,the actual biological systems may become cancerous or have randomness due to the influence of manipulated genes or external environmental stimuli.These phenomena make their logical dynamic system structure and analysis process complicated.In this thesis,we study the analysis,control and optimization of this kind of system with the tool of semi-tensor product of matrices,and apply the results to the game theory.The main research contents include: set stability(set stabilization)of Boolean(control)networks under constrained conditions,set stability of probabilistic multi-valued logical networks and optimal control of networked evolutionary game models.Details are as follows:1.The set stability and set stabilization of Boolean networks and Boolean control networks under constrained conditions are studied.The dynamical models of Boolean networks and Boolean control networks under conditional constraints are established,and the necessary and sufficient conditions for the stability(stabilization)of the(control)network from the initial set to the target set avoiding undesirable sets are given.By discussing the time for each state to reach the target set in the network model,a design method for finding the time optimal set stabilizer is proposed.2.The set stability of probabilistic multi-valued logical networks is studied.A matrix method is proposed to obtain the largest invariant subset contained in a given target set in probabilistic multi-valued logical network model.The stability of recurrent state equilibrium in state-based games is verified by the criterion proposed for probabilistic multi-valued logical networks.3.The strategy set optimization and optimal control problems for a class of networked evolutionary games with “myopic best response adjustment” are investigated.An algorithm for deleting dominated strategies is formulated for a given networked evolutionary game.The payoff optimization problem is considered by adding control players to the game and state feedback controls are designed to steer the game from an initial profile to the optimal profile which can maximize the long-term overall payoff of the whole game.