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Page 1
Fluctuating periodic solutions and moment boundedness of a stochastic model for the bone remodeling process.
Jerez S, Díaz-Infante S, Chen B. Jerez S, et al. Math Biosci. 2018 May;299:153-164. doi: 10.1016/j.mbs.2018.03.006. Epub 2018 Mar 8. Math Biosci. 2018. PMID: 29526549
We prove the existence of a globally attractive positive unique solution for the stochastically perturbed system. Also, the stochastic boundedness of the solution is demonstrated using its p-th order moments for p 1. Finally, we show that the in …
We prove the existence of a globally attractive positive unique solution for the stochastically perturbed system …
A series of population models for Hyphantria cunea with delay and seasonality.
Lu H, Song H, Zhu H. Lu H, et al. Math Biosci. 2017 Oct;292:57-66. doi: 10.1016/j.mbs.2017.07.010. Epub 2017 Jul 19. Math Biosci. 2017. PMID: 28735086
In this paper, we establish and study a basic stage-structured model for the population of Hyphantria cunea, a delay differential equation model and a model incorporating the resource and seasonality. By introducing the population reproduction number R(0), we show t …
In this paper, we establish and study a basic stage-structured model for the population of Hyphantria cunea, a delay differential …
Dynamical analysis of a stochastic non-autonomous SVIR model with multiple stages of vaccination.
Mehdaoui M, Alaoui AL, Tilioua M. Mehdaoui M, et al. J Appl Math Comput. 2023;69(2):2177-2206. doi: 10.1007/s12190-022-01828-6. Epub 2022 Dec 14. J Appl Math Comput. 2023. PMID: 36531662 Free PMC article.
For the proposed model, we prove the mathematical and biological well-posedness. That is, the existence of a unique global almost surely positive solution. Moreover, we establish conditions under which the disease vanishes or persists. Furthermore, bas …
For the proposed model, we prove the mathematical and biological well-posedness. That is, the existence of a unique global alm …
Dynamics of almost periodic Schoener's competition model with time delays and impulses.
Li C, Guo Z, Zhang Z. Li C, et al. Springerplus. 2016 Apr 14;5:447. doi: 10.1186/s40064-016-2068-x. eCollection 2016. Springerplus. 2016. PMID: 27119051 Free PMC article.
By using the comparison theorem and the Lyapunov functional method of the impulsive differential equations, some sufficient conditions are obtained for the persistence and existence of a unique uniformly asymptotically stable positive alm …
By using the comparison theorem and the Lyapunov functional method of the impulsive differential equations, some suffic …
Traveling wave solutions to a neural field model with oscillatory synaptic coupling types.
Dyson A. Dyson A. Math Biosci Eng. 2019 Jan 15;16(2):727-758. doi: 10.3934/mbe.2019035. Math Biosci Eng. 2019. PMID: 30861664 Free article.
With fronts as our main focus, we exploit Heaviside firing rate functions in order to establish existence and utilize speed index functions with at most one critical point as a tool for showing uniqueness of wave speed. We are able to construct Evans …
With fronts as our main focus, we exploit Heaviside firing rate functions in order to establish existence and utilize speed in …
The minimal model of the hypothalamic-pituitary-adrenal axis.
Vinther F, Andersen M, Ottesen JT. Vinther F, et al. J Math Biol. 2011 Oct;63(4):663-90. doi: 10.1007/s00285-010-0384-2. Epub 2010 Nov 24. J Math Biol. 2011. PMID: 21107577
The ultradian rhythm can mathematically be explained by oscillating solutions. Oscillating solutions to an ODE emerges from an unstable fixed point with complex eigenvalues with a positive real parts and a non-zero imaginary parts. ...Furthermore, this treatm …
The ultradian rhythm can mathematically be explained by oscillating solutions. Oscillating solutions to an ODE emerges from an …
On the dynamics of one-prey-n-predator impulsive reaction-diffusion predator-prey system with ratio-dependent functional response.
Liu Z, Zhang L, Bi P, Pang J, Li B, Fang C. Liu Z, et al. J Biol Dyn. 2018 Dec;12(1):551-576. doi: 10.1080/17513758.2018.1485974. J Biol Dyn. 2018. PMID: 29962293
On the basis of the upper and lower solution method and comparison theory of differential equation, sufficient conditions on the ultimate boundedness and permanence of the predator-prey system are established. By constructing an appropriate auxiliary funct …
On the basis of the upper and lower solution method and comparison theory of differential equation, sufficient conditio …
Periodic oscillations in leukopoiesis models with two delays.
Adimy M, Crauste F, Ruan S. Adimy M, et al. J Theor Biol. 2006 Sep 21;242(2):288-99. doi: 10.1016/j.jtbi.2006.02.020. Epub 2006 Apr 17. J Theor Biol. 2006. PMID: 16603196
We consider a nonlinear system of two equations, describing the evolution of a stem cell population and the resulting white blood cell population. ...We also prove the existence of a Hopf bifurcation which leads to periodic solutions. ...
We consider a nonlinear system of two equations, describing the evolution of a stem cell population and the resulting white bl …
On the almost periodic solution of cellular neural networks with distributed delays.
Liu Y, You Z, Cao L. Liu Y, et al. IEEE Trans Neural Netw. 2007 Jan;18(1):295-300. doi: 10.1109/TNN.2006.885441. IEEE Trans Neural Netw. 2007. PMID: 17278480
By exponential dichotomy about differential equations, a formal almost periodic solution (APS) of a class of cellular neural networks (CNNs) with distributed delays is obtained. Then, within different normed spaces, several sufficient conditions guaran …
By exponential dichotomy about differential equations, a formal almost periodic solution (APS) of a class of cel …
Almost periodic solution of non-autonomous Lotka-Volterra predator-prey dispersal system with delays.
Meng X, Chen L. Meng X, et al. J Theor Biol. 2006 Dec 21;243(4):562-74. doi: 10.1016/j.jtbi.2006.07.010. Epub 2006 Jul 20. J Theor Biol. 2006. PMID: 16934297
By using almost periodic functional hull theory, we show that the almost periodic system has a unique globally asymptotical stable strictly positive almost periodic solution. The conditions for the permanence, global stability of s …
By using almost periodic functional hull theory, we show that the almost periodic system has a unique globally a …