Complete dynamic analysis of homeostatic model: a feedback signal from extracellular matrix to FitzHugh–Nagumo neuron model

To examine the hemostatic behaviors of neural activity and extracellular matrix (ECM) molecules, this paper provides a mathematical model for ECM combined with a FitzHugh–Nagumo neuronal model. The dynamic behaviors of the proposed model are investigated utilizing dynamical tools such as Lyapunov exponents and bifurcation diagrams. The basin attractions of the ECM molecule and protease models were also studied. The presented model demonstrates the coexistence of periodic and chaotic dynamics, which are thought to be distinct modulation modes of neuronal circuits in ECM. Finally, the master stability function is used to examine the synchronization characteristics of the two coupled systems. It is discovered that the coupling configurations of protease concentration to the protease concentration, protease concentration to the potential membrane of the neuron, and the potential membrane of the neuron to the ECM concentration variables can synchronize the coupled models. This research will help neurologists investigate numerous rhythms in the brain and their roles.