Jacobian-based feedback control of random boolean networks

A feedback control scheme to shift the phase of random boolean networks (RBNs) from disorder to order is proposed. A Jacobian matrix is calculated based on the state and Boolean function of each node at each step. A control scheme is proposed by using a greedy algorithm to select the minimum number of nodes to be frozen so as to reduce effectively the number of 1´s in the Jacobian of the remaining nodes, which renders the Lyapunov exponent to be negative. Simulation results show that the dynamics of the controlled RBN is periodic or convergent to a fixed point.