Stability of limit cycles in a pluripotent stem cell dynamics model

TL;DR

This paper analyzes the stability of limit cycles in a delay differential equation model of pluripotent stem cell populations, identifying conditions for stability loss via Hopf bifurcation and validating findings with numerical simulations.

Contribution

It provides a detailed stability analysis of limit cycles in a nonlinear delay differential equation model for stem cell dynamics, including bifurcation analysis and numerical validation.

Findings

Unique nontrivial equilibrium stability conditions identified

Stability loss through Hopf bifurcation demonstrated

Numerical simulations support theoretical results

Abstract

This paper is devoted to the study of the stability of limit cycles of a nonlinear delay differential equation with a distributed delay. The equation arises from a model of population dynamics describing the evolution of a pluripotent stem cells population. We study the local asymptotic stability of the unique nontrivial equilibrium of the delay equation and we show that its stability can be lost through a Hopf bifurcation. We then investigate the stability of the limit cycles yielded by the bifurcation using the normal form theory and the center manifold theorem. We illustrate our results with some numerics.