Dynamical analysis of a fractional discrete-time vocal system

The study in this article aims at investigating the chaotic behavior of the 2-D vocal dynamical system using commensurate and incommensurate fractional order Caputo difference operator. Dynamics of the discrete fractional order 2-D vocal dynamical system is analysed with bifurcation, Lyapunov exponents and coexisting attractors. Stability analysis for both commensurate and incommensurate order of the model is performed at unique fixed point supported with numerical calculation and simulations. The importance of constructing real-life models with incommensurate order models is illustrated by means of bifurcation diagrams and phase plane diagrams. The article focuses on analysis of change in the behaviour of the system dynamics under the influence of fractional order of the system, thereby showcasing the advantages of employing discrete fractional operators towards modelling. Article also portrays the transition that occurs on the vibration of the tissues in vocal fold in comparison with obtained theoretical mathematical and numerical results.

Automated summary

This article investigates the chaotic behavior of the 2-D vocal dynamical system using commensurate and incommensurate fractional order Caputo difference operator. The analysis shows that the behavior of the system changes with different fractional orders, highlighting the importance of employing incommensurate order models in real-life modeling.