This paper investigates a three-species reaction-diffusion model with fractional-order derivatives and proposes an innovative numerical method for its simulation. The method integrates an optimized Grünwald-Letnikov discretization scheme, enhanced by a short-memory principle, with a high-order accurate nine-point compact difference scheme, enabling an efficient and stable solution of fractional operators. Rigorous convergence and stability analyses confirm the theoretical reliability of the algorithm. Through stability and Turing bifurcation analyses, the study systematically reveals the regulatory mechanism of the fractional-order exponent on the dynamic behavior of the system. The numerical results demonstrate that the present method accurately captures the effect of fractional derivatives on the formation process of spatial patterns.

This paper investigates the chaotic dynamics in a fractional-order vocal fold vibration (VCV) model based on the Grünwald-Letnikov fractional derivative (GLFD). Studying the characteristics of vocal fold vibration is of great significance for revealing its vibration mechanism, the etiology of abnormal vibrations, and natural speech synthesis. Traditional vocal fold vibration models are based on integer-order systems and are unable to describe the memory effects present in real physical systems. To overcome this limitation, this paper introduces fractional derivatives and develops a high-precision numerical method to simulate the fractional-order VCV model. By incorporating nonlinear elastic and damping forces, the model can more accurately describe the complex dynamic characteristics of vocal fold vibrations, including memory effects and non-locality. The numerical simulation results reveal novel chaotic behaviors in the fractional-order VCV model, which have not been observed in integer-order models. These findings provide new insights into the possible dynamic states of vocal fold vibrations and lay the foundation for further theoretical and experimental studies on the vocal cord vibration mechanism.