{"title":"Dynamics of a pituitary–adrenal model with distributed time delays","authors":"Eva Kaslik , Maria Roxana Matei , Mihaela Neamţu","doi":"10.1016/j.cnsns.2024.108363","DOIUrl":null,"url":null,"abstract":"<div><div>This paper investigates the effects of distributed time delays on the dynamics of the pituitary–adrenal axis. Our two-dimensional model incorporates distributed time delays with general delay kernels, specifically illustrating interactions between adrenocorticotropic hormone (ACTH) and cortisol (CORT). We derive general theoretical results for general delay kernels, exemplified by Dirac and weak Gamma kernels, revealing stability transitions characterized by Hopf bifurcations. We establish conditions for the local asymptotic stability of the unique equilibrium and discuss the existence of periodic solutions. Numerical simulations demonstrate that periodic oscillations appear for appropriate values of the average time delays. Including an external input results in both ultradian and circadian rhythms, highlighting the system’s dynamic responsiveness to external stimuli.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4000,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Nonlinear Science and Numerical Simulation","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1007570424005483","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
This paper investigates the effects of distributed time delays on the dynamics of the pituitary–adrenal axis. Our two-dimensional model incorporates distributed time delays with general delay kernels, specifically illustrating interactions between adrenocorticotropic hormone (ACTH) and cortisol (CORT). We derive general theoretical results for general delay kernels, exemplified by Dirac and weak Gamma kernels, revealing stability transitions characterized by Hopf bifurcations. We establish conditions for the local asymptotic stability of the unique equilibrium and discuss the existence of periodic solutions. Numerical simulations demonstrate that periodic oscillations appear for appropriate values of the average time delays. Including an external input results in both ultradian and circadian rhythms, highlighting the system’s dynamic responsiveness to external stimuli.
期刊介绍：
The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity.
The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged.
Topics of interest:
Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity.
No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.
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