Optimal mixed control of networked reaction-diffusion systems

We introduce a control scheme able to steer the evolution of networked reaction-diffusion systems toward any intended dynamics. Specifically, we consider simplicial complexes of reaction-diffusion systems that can be collapsed into weighted complex networks by leveraging the linear relationship between the Laplacian matrix of the simplicial complex and the Laplacian matrix of each order simplex. The method integrates reaction and network-based diffusion controls and, as far as effectiveness and cost are concerned, features a significantly improved performance over traditional single-variable control methods. Numerical simulations using the FitzHugh-Nagumo and susceptible-infected-removed models demonstrate the resilience of the proposed mixed control across diverse systems, highlighting the potential of the method for complex system management and intervention strategies.