Synchronization of cells with activator-inhibitor pathways through adaptive environment-mediated coupling

In this paper, we report the synchronized dynamics of cells with activator-inhibitor pathways via an adaptive environment-mediated coupling scheme with feedbacks and control mechanisms. The adaptive character of the extracellular medium is modeled via its damping parameter as a physiological response aiming at annihilating the cellular differentiation existing between the chaotic biochemical pathways of the cells, in order to preserve homeostasis. We perform an investigation on the existence and stability of the synchronization manifold of the coupled system under the proposed coupling pattern. Both mathematical and computational tools suggest the accessibility of conducive prerequisites (conditions) for the emergence of a robust synchronous regime. The relevance of a phase-synchronized dynamics is appraised and several numerical indicators advocate for the prevalence of this fascinating phenomenon among the interacting cells in the phase space.