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Stability of limit cycles in a pluripotent stem cell dynamics model

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.
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Submitted on : Thursday, April 16, 2009 - 2:55:59 PM
Last modification on : Monday, November 7, 2022 - 5:24:33 PM
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Mostafa Adimy, Fabien Crauste, Andrei Halanay, Mihaela Neamtu, Dumitru Opris. Stability of limit cycles in a pluripotent stem cell dynamics model. Chaos, Solitons & Fractals, 2006, 27 (4), pp.1091-1107. ⟨10.1016/j.chaos.2005.04.083⟩. ⟨hal-00376002⟩

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