Positive Stability Analysis and Bio-Circuit Design for Nonlinear Biochemical Networks

This paper is concerned with positive stability analysis and bio-circuits design for nonlinear biochemical networks. A fuzzy interpolation approach is employed to approximate nonlinear biochemical networks. Based on the Lyapunov stability theory, sufficient conditions are developed to guarantee the equilibrium points of nonlinear biochemical networks to be positive and asymptotically stable. In addition, a constrained bio-circuits design with positive control input is also considered. It is shown that the conditions can be formulated as a solution to a convex optimization problem, which can be easily facilitated by using the Matlab LMI control toolbox. Finally, a real biochemical network model is provided to illustrate the effectiveness and validity of the obtained results

Entrained Collective Rhythms of Multicellular Systems: Partial Impulsive Control Strategy

This paper is concerned with the study of entrained collective rhythms of multicellular systems by using partial impulsive control strategy. The objective is to design an impulsive controller based on only those partially available cell states, so that the entrained collective rhythms are guaranteed for the multicellular systems with cell-to-cell communication mechanism. By using the newly developed impulsive integrodifferential inequality, the sufficient conditions are derived to achieve the entrained collective rhythms of multicellular systems. A synthetic multicellular system with simulation results is finally given to illustrate the usefulness of the developed results