Work

Numerical simulation of chaotic dynamics in a fractional-order vibration model with Grünwald-Letnikov fractional derivative

Year: 2025

Type: article

Abstract: 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.

Source: Networks and Heterogeneous Media

DOI: 10.3934/nhm.2025027

Authors: Jiaxin Zhang, Wei Zhang, Xiaoyu Li

Institutions: Anhui University of Science and Technology, Anhui Science and Technology University, Jining Normal University, Inner Mongolia University of Technology

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: Inner Mongolia University, Natural Science Foundation of Inner Mongolia, Inner Mongolia University of Technology

Awards: G1133555592, G3631968142, G6722492483