Synchronization of discrete time fractional order neuromuscular models in the presence and absence of stimulus

This article proposes a fractional order discrete-time neuromuscular model incorporating calcium kinetics to study the essential role of the neuromuscular system in facilitating rapid information transmission between nerve cells and muscles for bodily functions. The study conducts a dynamical analysis to investigate the stability and periodic oscillations of the system in the presence and absence of tetanus stimuli from neurons. Bifurcation diagrams are generated for different fractional orders and rate constants, highlighting the occurrence of chaotic dynamics. The region of chaos is determined using the largest Lyapunov exponents and the Jacobian matrix method. The study also achieves synchronization of the systems by employing nonlinear control functions with feedback gains. Emphasizing the significance of constructing the biological model using fractional order operators, the article provides a chemical interpretation of the analytical findings. Moreover, the article employs dynamic plots to visually depict the changing system variables over time, allowing for an examination of the concurrent presence of multiple attractors through bifurcation diagrams and phase plane portraits. By studying how chemical kinetics and muscle activation are interrelated, the article uncovers captivating revelations that could guide the formulation of strategies to combat muscle disorders. The article also underscores the potential utility of synchronization in managing neuromuscular conditions, thus emphasizing its practical implications in disease control.