Passivity of delayed reaction-diffusion networks with application to a food web model

This paper is concerned with the passivity problem of a class of delayed reaction-diffusion networks, in which the input and output variables are varied with the time and space variables. Firstly, two new passivity definitions are proposed, which are totally different from some existing concepts of passivity. Then we establish several criteria for the passivity, input strict passivity and output strict passivity by using the Lyapunov functional method combined with the inequality techniques, and also reveal the relationship between passivity and stability of the reaction-diffusion networks. Moreover, these results are applied to investigate the asymptotic stability and control design of a food web model with time delay and reaction-diffusion terms. Numerical simulations are presented finally to demonstrate the effectiveness of the proposed results.