In this work, we focus on the reduction of network communication burden of cooperative distributed model predictive control (DMPC) of a class of nonlinear processes. Specifically, we propose a cooperative DMPC design in which the evaluations of the distributed controllers are triggered by the difference between the subsystem state measurements and the estimates of them. The individual model predictive controllers in this DMPC are designed via Lyapunov techniques. Under the assumption that state measurements of the subsystems are available, sufficient conditions for the closed-loop stability are derived. The proposed DMPC is applied to a reactor-separator chemical process example and is compared with a cooperative DMPC in which distributed controllers are evaluated every sampling time extensively. The results demonstrate the applicability and effectiveness of the proposed approach.