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The Selkov system, which is typically employed to model glycolysis phenomena, unveils some rich dynamics and some other complex formations in biochemical reactions. In the present work, the synchronization problem of the glycolysis reaction-diffusion model is handled and examined. In addition, a novel convenient control law is designed in a linear form and, on the other hand, the stability of the associated error system is demonstrated through utilizing a suitable Lyapunov function. To illustrate the applicability of the proposed schemes, several numerical simulations are performed in one- and two-spatial dimensions. [ABSTRACT FROM AUTHOR]

In this paper, dynamical behavior and synchronization of a non-equilibrium four-dimensional chaotic system are studied. The system only includes one constant term and has hidden attractors. Some dynamical features of the governing system, such as invariance and symmetry, the existence of attractors and dissipativity, chaotic flow with a plane of equilibria, and offset boosting of the chaotic attractor, are stated and discussed and a new disturbance-observer-based adaptive terminal sliding mode control (ATSMC) method with input saturation is proposed for the control and synchronization of the chaotic system. To deal with unexpected noises, an extended Kalman filter (EKF) is implemented along with the designed controller. Through the concept of Lyapunov stability, the proposed control technique guarantees the finite time convergence of the uncertain system in the presence of disturbances and control input limits. Furthermore, to decrease the chattering phenomena, a genetic algorithm is used to optimize the controller parameters. Finally, numerical simulations are presented to demonstrate the performance of the designed control scheme in the presence of noise, disturbances, and control input saturation. [ABSTRACT FROM AUTHOR]