Periodically stimulated remodelling of a muscle fibre: perturbation analysis of a simple system of first-order ODEs

Abstract

The paper deals with the dynamical analysis of the system of first-order ODE’s describing the isometric stimulation of the muscle fibre. This system is considered to be a non-autonomous one having the periodical excitation. For the analysis of dynamical behaviour the system the multiple scale method (MSM) is employed. The main goal of this contribution is to show the application of MSM to the non-autonomous dynamical system using the first order approximation of the solution. The existence of the degenerated Hopf’s bifurcation of the gained solution is presented.

Keywords

• Dynamical non-autonomous system
• Muscle fibre
• Multi-scale method
• Hopf’s bifurcation
• Chaos