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Journal of Applied Nonlinear Dynamics 12(4) (2023) 781--797 | DOI:10.5890/JAND.2023.12.011

S. El Fadily

LERMA, Mohammadia School of engineering, Mohammed V University, Rabat, Morocco

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Abstract

This article is a generalized study of the dynamics of a delayed Solow model with a structured population. Within this framework, we investigate the linear stability and the existence of a Hopf bifurcation. We show that Hopf bifurcations occur as a $\tau$-delay passes through critical values. Then using the standard form theory and center form reduction, we drive an explicit algorithm that allows determining the direction of Hopf bifurcation and the stability of the resulting periodic solutions. We give some numerical examples to motivate the proposal and illustrate our results.

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