Chaos dynamics and pyragas control in a three-variable chemical reaction system

Abstract Nonlinear dynamics and chaotic phenomena are inherent in many complex chemical and biochemical systems, and their effective control is crucial for optimizing industrial processes. However, the proficient management of chaotic regimes and a comprehensive understanding of dynamic transitions in models featuring autocatalysis and saturation terms remain significant challenges. This study investigated the nonlinear behavior of a three-dimensional chemical model, aiming to identify chaotic regimes and apply an effective control strategy for their suppression. The dynamics of this model, which describes the temporal evolution of three intermediate species coupled by autocatalysis and Michaelis–Menten type saturation terms, were qualitatively analyzed through bifurcation diagrams and quantitatively by Lyapunov exponents. Pyragas’ Time-Delayed Auto-Synchronization (TDAS) method was non-invasively applied to stabilize unstable periodic orbits. The results revealed a classical route to chaos via period-doubling bifurcations and exhibited extreme sensitivity to initial conditions. Simulations confirmed the effectiveness of TDAS in regularizing the system’s dynamics, successfully stabilizing unstable periodic orbits, and rendering the behavior predictable without altering the intrinsic structure of the system. This study enhances the design and operation of industrial processes, as the identification of chaotic regimes and their transition routes allows for avoiding undesirable operating conditions and maintaining stable oscillatory regimes, thereby increasing safety, reproducibility, and efficiency. The findings are relevant for nonlinear chemical and biochemical reactions in continuous reactors and complex catalytic systems.