Bifurcation Analysis and Diffusion‐Driven Instability of the Spatiotemporal Degn–Harrison Model

This paper investigates the dynamical behavior of a nonlinear model based on the Degn–Harrison formulation, using both theoretical and numerical methods. The study focuses on analyzing the stability characteristics and pattern formation of the model. Local stability is evaluated by linearizing the system around steady states. Conditions for the onset of Hopf bifurcation (HB) are derived, highlighting the transition from steady states to oscillatory dynamics. Additionally, the role of spatial effects is examined by incorporating diffusion terms, offering insights into diffusion‐induced instability and the development of spatial patterns. Numerical simulations are conducted to validate the analytical results and assess the system’s robustness against parameter variations. The combined analysis of stability, bifurcation, and diffusion‐driven dynamics provides a comprehensive understanding of the Degn–Harrison framework. This work contributes to the theoretical and computational understanding of nonlinear dynamics in reaction–diffusion (RD) systems.