Network dynamics of a periodically forced chemical system and its application for tuning PID controller with time-delay systems

In this paper, network dynamics are investigated in a periodically forced chemical system. At the same time, the ring network and ring-star network based on the periodically forced chemical system are designed. The chaotic dynamics of the ring network and ring-star network are analyzed by using the Lyapunov exponent spectrum, bifurcation diagram and correlation function. We show that the coupling strength of ring network has an important influence on chaotic dynamics and synchronization. By comparing ten, eleven and 100 nodes, we find that the bifurcation path of the ring-star network is robust to the number of nodes, which is different from the ring network. In addition, the ring-star network in comparison with the ring network achieved chaotic complete synchronization among all nodes. Finally, we proposed a new chaotic whale optimization (CWO) algorithm using the randomness of the ring-star network. It is used to tune the parameters of the PID controller with large time-delay systems. The simulation results show that the proposed CWO algorithm presents better performance than other available algorithms in the literature.