On the Stability and Control of the Willamowski–Rössler Chaotic Reaction Model

Abstract

ABSTRACT This paper investigates the stability and dynamic behavior of the Willamowski–Rössler (WR) chemical reaction model, a classical prototype for chaotic oscillations in chemical kinetics. While previous studies have primarily focused on isolated equilibria or local dynamical properties, this work provides a systematic and unified analysis of the WR model by characterizing the full coexistence structure of its equilibria and rigorously determining their stability across distinct parameter regions. In particular, we identify regions of full and partial equilibrium coexistence and derive exact analytical conditions for the occurrence of Hopf bifurcations, thereby clarifying the parameter regimes in which oscillatory and chaotic dynamics may arise. This framework yields a global perspective on the stability landscape of the WR system that is not available in earlier analyses. In addition, two backstepping‐based control schemes are developed to achieve stabilization and master‐slave synchronization of the WR model. Numerical simulations are presented to validate the theoretical results and demonstrate the effectiveness of the proposed control strategies. The results contribute to a deeper understanding of the WR system's dynamics and provide a structured basis for control‐oriented applications in chemical reaction engineering.