title: Stability and Hopf bifurcation analysis for the hypothalamic-pituitary-adrenal axis model with memory.
abstract: This article generalizes the existing minimal model of the hypothalamic-pituitary-adrenal (HPA) axis in a realistic way, by including memory terms: distributed time delays, on one hand and fractional-order derivatives, on the other hand. The existence of a unique equilibrium point of the mathematical models is proved and a local stability analysis is undertaken for the system with general distributed delays. A thorough bifurcation analysis for the distributed delay model with several types of delay kernels is provided. Numerical simulations are carried out for the distributed delays models and for the fractional-order model with discrete delays, which substantiate the theoretical findings. It is shown that these models are able to capture the vital mechanisms of the HPA system.
authors.affiliation: Department of Mathematics and Computer Science, West University of Timişoara, Romania.|Institute e-Austria Timisoara, cam. 045B, Romania.
authors.forename: Eva
authors.initials: E
authors.lastname: Kaslik
authors.affiliation: Department of Economics and Modelling, West University of Timişoara, Romania.|University Politehnica of Bucharest, Bucharest, Romania.
authors.forename: Mihaela
authors.initials: M
authors.lastname: Neamtu
mesh_terms: D006801:Humans; D007030:Hypothalamo-Hypophyseal System; D008962:Models, Theoretical; D010913:Pituitary-Adrenal System