International Journal of Nonlinear Analysis and Applications

Bifurcation and chaos in a one mass discrete time vocal fold dynamical model

Document Type : Research Paper

Authors

1 Department of Mathematics, Yazd University, Yazd, Iran

2 Department of Mathematics, Yazd University, Yazd, Iran.

Abstract

In this article, we are going to study the stability and bifurcation of a two-dimensional discrete time vocal fold model. The existence and local stability of the unique fixed point of the model is investigated. It is shown that a Neimark-Sacker bifurcation occurs and an invariant circle will appear. We give sufficient conditions for this system to be chaotic in the sense of Marotto. Numerically it is shown that our model has positive Lyapunov exponent and is sensitive dependence on initial conditions. Some numerical simulations are presented to illustrate our theoretical results.

Keywords

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International Journal of Nonlinear Analysis and Applications
Volume 12, Issue 2
November 2021
Pages 305-315
  • Receive Date: 24 December 2019
  • Revise Date: 05 May 2020
  • Accept Date: 08 June 2020