23 results match your criteria Advances In Difference Equations[Journal]

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Andronov-Hopf and Neimark-Sacker bifurcations in time-delay differential equations and difference equations with applications to models for diseases and animal populations.

Adv Differ Equ 2020 29;2020(1):190. Epub 2020 Apr 29.

2Department of Mathematics, King Mongkuts University of Technology North Bangkok, Bangkok, Thailand.

In many areas, researchers might think that a differential equation model is required, but one might be forced to use an approximate difference equation model if data is only available at discrete points in time. In this paper, a detailed comparison is given of the behavior of continuous and discrete models for two representative time-delay models, namely a model for HIV and an extended logistic growth model. For each model, there are seven different time-delay versions because there are seven different positions to include time delays. Read More

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http://dx.doi.org/10.1186/s13662-020-02646-5DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7223581PMC

A stochastic SIR epidemic model with Lévy jump and media coverage.

Adv Differ Equ 2020 12;2020(1):70. Epub 2020 Feb 12.

1College of Mathematics and Computer Science, Gannan Normal University, Ganzhou, P.R. China.

A stochastic susceptible-infectious-recovered epidemic model with temporary immunity and media coverage is proposed. The effects of Lévy jumps on the dynamics of the model are considered. A unique global positive solution for the epidemic model is obtained. Read More

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http://dx.doi.org/10.1186/s13662-020-2521-6DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7224063PMC
February 2020

Monotonicity properties for a ratio of finite many gamma functions.

Authors:
Feng Qi Dongkyu Lim

Adv Differ Equ 2020 1;2020(1):193. Epub 2020 May 1.

4Department of Mathematics Education, Andong National University, Andong, Republic of Korea.

In the paper, the authors consider a ratio of finite many gamma functions and find its monotonicity properties such as complete monotonicity, the Bernstein function property, and logarithmically complete monotonicity. Read More

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http://dx.doi.org/10.1186/s13662-020-02655-4DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7194249PMC

Dynamics analysis of a delayed virus model with two different transmission methods and treatments.

Adv Differ Equ 2020 6;2020(1). Epub 2020 Jan 6.

1College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, P.R. China.

In this paper, a delayed virus model with two different transmission methods and treatments is investigated. This model is a time-delayed version of the model in (Zhang et al. in Comput. Read More

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http://dx.doi.org/10.1186/s13662-019-2438-0DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7100214PMC
January 2020

Global stability analysis for a generalized delayed SIR model with vaccination and treatment.

Adv Differ Equ 2019 21;2019(1):532. Epub 2019 Dec 21.

3Department of Mathematical Sciences, United Arab Emirates University, Al Ain, United Arab Emirates.

In this work, we investigate the stability of an SIR epidemic model with a generalized nonlinear incidence rate and distributed delay. The model also includes vaccination term and general treatment function, which are the two principal control measurements to reduce the disease burden. Using the Lyapunov functions, we show that the disease-free equilibrium state is globally asymptotically stable if , where is the basic reproduction number. Read More

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http://dx.doi.org/10.1186/s13662-019-2447-zDOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7100696PMC
December 2019

Global exponential stability of Markovian jumping stochastic impulsive uncertain BAM neural networks with leakage, mixed time delays, and -inverse Hölder activation functions.

Adv Differ Equ 2018 27;2018(1):113. Epub 2018 Mar 27.

5Department of Mathematics, Faculty of Science, Maejo University, Chiang Mai, Thailand.

This paper concerns the problem of enhanced results on robust finite time passivity for uncertain discrete time Markovian jumping BAM delayed neural networks with leakage delay. By implementing a proper Lyapunov-Krasovskii functional candidate, reciprocally convex combination method, and linear matrix inequality technique, we derive several sufficient conditions for varying the passivity of discrete time BAM neural networks. Further, some sufficient conditions for finite time boundedness and passivity for uncertainties are proposed by employing zero inequalities. Read More

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http://dx.doi.org/10.1186/s13662-018-1553-7DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5942391PMC
March 2018
3 Reads

Entire solutions for a reaction-diffusion equation with doubly degenerate nonlinearity.

Authors:
Rui Yan Xiaocui Li

Adv Differ Equ 2018 24;2018(1):147. Epub 2018 Apr 24.

2School of Science, Beijing University of Chemical Technology, Beijing, P.R. China.

This paper is concerned with the existence of entire solutions for a reaction-diffusion equation with doubly degenerate nonlinearity. Here the entire solutions are the classical solutions that exist for all [Formula: see text]. With the aid of the comparison theorem and the sup-sub solutions method, we construct some entire solutions that behave as two opposite traveling front solutions with critical speeds moving towards each other from both sides of -axis and then annihilating. Read More

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https://advancesindifferenceequations.springeropen.com/artic
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http://dx.doi.org/10.1186/s13662-018-1606-yDOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5915528PMC
April 2018
16 Reads

Approximation of state variables for discrete-time stochastic genetic regulatory networks with leakage, distributed, and probabilistic measurement delays: a robust stability problem.

Adv Differ Equ 2018 3;2018(1):123. Epub 2018 Apr 3.

5Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia.

This work predominantly labels the problem of approximation of state variables for discrete-time stochastic genetic regulatory networks with leakage, distributed, and probabilistic measurement delays. Here we design a linear estimator in such a way that the absorption of mRNA and protein can be approximated via known measurement outputs. By utilizing a Lyapunov-Krasovskii functional and some stochastic analysis execution, we obtain the stability formula of the estimation error systems in the structure of linear matrix inequalities under which the estimation error dynamics is robustly exponentially stable. Read More

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http://dx.doi.org/10.1186/s13662-018-1569-zDOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5882887PMC
April 2018
2 Reads

Extensions of the natural approach to refinements and generalizations of some trigonometric inequalities.

Adv Differ Equ 2018 14;2018(1):90. Epub 2018 Mar 14.

2Valahia University of Târgovişte, Târgovişte, Romania.

In this paper we propose a new method for sharpening and refinements of some trigonometric inequalities. We apply these ideas to some inequalities of Wilker-Cusa-Huygens type. Read More

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http://dx.doi.org/10.1186/s13662-018-1545-7DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5852252PMC
March 2018
3 Reads

Hopf bifurcation analysis of a delayed SEIR epidemic model with infectious force in latent and infected period.

Adv Differ Equ 2018 1;2018(1):348. Epub 2018 Oct 1.

Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi, Bangkok, Thailand.

In this paper, we analyze a delayed epidemic model in which the latent and infected states are infective. The model has a globally asymptotically stable disease-free equilibrium whenever a certain epidemiological threshold, known as the basic reproduction number , is less than or equal to unity. We investigate the effect of the time delay on the stability of endemic equilibrium when . Read More

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http://dx.doi.org/10.1186/s13662-018-1805-6DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7099316PMC
October 2018

Moment closure of infectious diseases model on heterogeneous metapopulation network.

Adv Differ Equ 2018 24;2018(1):339. Epub 2018 Sep 24.

2Complex Systems Research Center, Shanxi University, Taiyuan, China.

The global transmission of infectious diseases poses huge threats to human. Traditional heterogeneous mean-field models on metapopulation networks ignore the heterogeneity of individuals who are in different disease states in subpopulations with the same degree, resulting in inaccuracy in predicting the spread of disease. In this paper, we take heterogeneity of susceptible and infectious individuals in subpopulations with the same degree into account, and propose a deterministic unclosed general model according to Markov process on metapopulation networks to curve the global transmission of diseases precisely. Read More

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http://dx.doi.org/10.1186/s13662-018-1801-xDOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7100108PMC
September 2018

A discrete-time analog for coupled within-host and between-host dynamics in environmentally driven infectious disease.

Adv Differ Equ 2018 26;2018(1):69. Epub 2018 Feb 26.

College of Mathematics and Systems Science, Xinjiang University, Urumqi, People's Republic of China.

In this paper, we establish a discrete-time analog for coupled within-host and between-host systems for an environmentally driven infectious disease with fast and slow two time scales by using the non-standard finite difference scheme. The system is divided into a fast time system and a slow time system by using the idea of limit equations. For the fast system, the positivity and boundedness of the solutions, the basic reproduction number and the existence for infection-free and unique virus infectious equilibria are obtained, and the threshold conditions on the local stability of equilibria are established. Read More

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http://dx.doi.org/10.1186/s13662-018-1522-1DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7100524PMC
February 2018

The mean value theorem and Taylor's theorem for fractional derivatives with Mittag-Leffler kernel.

Adv Differ Equ 2018 9;2018(1):86. Epub 2018 Mar 9.

2Department of Mathematics, Cankaya University, Ankara, Turkey.

We establish analogues of the mean value theorem and Taylor's theorem for fractional differential operators defined using a Mittag-Leffler kernel. We formulate a new model for the fractional Boussinesq equation by using this new Taylor series expansion. Read More

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http://dx.doi.org/10.1186/s13662-018-1543-9DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6566265PMC
March 2018
1 Read

Enhanced robust finite-time passivity for Markovian jumping discrete-time BAM neural networks with leakage delay.

Adv Differ Equ 2017 10;2017(1):318. Epub 2017 Oct 10.

Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, King Abdulaziz University, Jeddah, 21589 Saudi Arabia.

This paper is concerned with the problem of enhanced results on robust finite-time passivity for uncertain discrete-time Markovian jumping BAM delayed neural networks with leakage delay. By implementing a proper Lyapunov-Krasovskii functional candidate, the reciprocally convex combination method together with linear matrix inequality technique, several sufficient conditions are derived for varying the passivity of discrete-time BAM neural networks. An important feature presented in our paper is that we utilize the reciprocally convex combination lemma in the main section and the relevance of that lemma arises from the derivation of stability by using Jensen's inequality. Read More

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http://dx.doi.org/10.1186/s13662-017-1378-9DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5635139PMC
October 2017
4 Reads

Entire functions sharing a small function with their two difference operators.

Adv Differ Equ 2017 1;2017(1):216. Epub 2017 Aug 1.

Department of Mathematics, Wuyi University, Jiangmen, Guangdong 529020 P.R. China.

In this article, we deduce a uniqueness result of entire functions that share a small entire function with their two difference operators, generalizing some previous theorems of (Farissi et al. in Complex Anal. Oper. Read More

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http://dx.doi.org/10.1186/s13662-017-1281-4DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5539324PMC
August 2017
14 Reads

A multi-regions discrete-time epidemic model with a travel-blocking vicinity optimal control approach on patches.

Adv Differ Equ 2017 26;2017(1):120. Epub 2017 Apr 26.

2Laboratory of Algebra, Analysis and Applications (L3A), Department of Mathematics and Computer Science, Hassan II University of Casablanca, Sidi Othman, BP 7955, Casablanca, Morocco.

We study, in this paper, infection dynamics when an epidemic emerges to many regions which are connected with their neighbors by any kind of anthropological movement. For this, we devise a multi-regions discrete-time model with the three classical SIR compartments, describing the spatial-temporal behaviors of homogenous susceptible, infected and removed populations. We suppose a large geographical domain, presented by a grid of colored cells, to exhibit at each instant the spatial propagation of an epidemic which affects its different parts or sub-domains that we call here cells or regions. Read More

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http://dx.doi.org/10.1186/s13662-017-1168-4DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7099345PMC

Fuzzy [Formula: see text] output-feedback control for the discrete-time system with channel fadings, sector nonlinearities, and randomly occurring interval delays and nonlinearities.

Adv Differ Equ 2016 21;2016(1):267. Epub 2016 Oct 21.

School of Science, Jiangnan University, Wuxi, 214122 China ; Key Laboratory of Advanced Process Control for Light Industry, Ministry of Education, Institute of Automation, Jiangnan University, Wuxi, 214122 China.

In this paper, the fuzzy [Formula: see text] output-feedback control problem is investigated for a class of discrete-time T-S fuzzy systems with channel fadings, sector nonlinearities, randomly occurring interval delays (ROIDs) and randomly occurring nonlinearities (RONs). A series of variables of the randomly occurring phenomena obeying the Bernoulli distribution is used to govern ROIDs and RONs. Meanwhile, the measurement outputs are subject to the sector nonlinearities ( the sensor saturations) and we assume the system output is [Formula: see text], [Formula: see text]. Read More

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http://dx.doi.org/10.1186/s13662-016-0991-3DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5075028PMC
October 2016
2 Reads

The stability of a predator-prey system with linear mass-action functional response perturbed by white noise.

Adv Differ Equ 2016;2016:54. Epub 2016 Feb 18.

School of College of Basic Sciences, Changchun University of Technology, Changchun, 130021 China.

The present paper deals with the problem of an ecoepidemiological model with linear mass-action functional response perturbed by white noise. The essential mathematical features are analyzed with the help of the stochastic stability, its long time behavior around the equilibrium of deterministic ecoepidemiological model, and the stochastic asymptotic stability by Lyapunov analysis methods. Numerical simulations for a hypothetical set of parameter values are presented to illustrate the analytical findings. Read More

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http://dx.doi.org/10.1186/s13662-016-0776-8DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4762146PMC
February 2016
8 Reads

Global dynamics for discrete-time analog of viral infection model with nonlinear incidence and CTL immune response.

Adv Differ Equ 2016 23;2016(1):143. Epub 2016 May 23.

College of Mathematics and Systems Science, Xinjiang University, Urumqi, 830046 People's Republic of China.

In this paper, a discrete-time analog of a viral infection model with nonlinear incidence and CTL immune response is established by using the Micken non-standard finite difference scheme. The two basic reproduction numbers and are defined. The basic properties on the positivity and boundedness of solutions and the existence of the virus-free, the no-immune, and the infected equilibria are established. Read More

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http://dx.doi.org/10.1186/s13662-016-0862-yDOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7099752PMC

Global dynamics for a class of discrete SEIRS epidemic models with general nonlinear incidence.

Adv Differ Equ 2016 6;2016(1):123. Epub 2016 May 6.

1College of Mathematics and System Sciences, Xinjiang University, Urumqi, 830046 People's Republic of China.

In this paper, a class of discrete SEIRS epidemic models with general nonlinear incidence is investigated. Particularly, a discrete SEIRS epidemic model with standard incidence is also considered. The positivity and boundedness of solutions with positive initial conditions are obtained. Read More

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http://dx.doi.org/10.1186/s13662-016-0846-yDOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7100848PMC

Hybrid control of the Neimark-Sacker bifurcation in a delayed Nicholson's blowflies equation.

Adv Differ Equ 2015;2015:306. Epub 2015 Oct 6.

School of Science, Qingdao Technological University, Qingdao, 266033 P.R. China.

In this article, for delayed Nicholson's blowflies equation, we propose a hybrid control nonstandard finite-difference (NSFD) scheme in which state feedback and parameter perturbation are used to control the Neimark-Sacker bifurcation. Firstly, the local stability of the positive equilibria for hybrid control delay differential equation is discussed according to Hopf bifurcation theory. Then, for any step-size, a hybrid control numerical algorithm is introduced to generate the Neimark-Sacker bifurcation at a desired point. Read More

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http://dx.doi.org/10.1186/s13662-015-0640-2DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4762134PMC
October 2015
9 Reads

Global stability of the endemic equilibrium of a discrete SIR epidemic model.

Adv Differ Equ 2013 25;2013(1):42. Epub 2013 Feb 25.

2School of Science, Shaanxi University of Science & Technology, Xi'an, 710021 China.

The basic reproductive number of a discrete SIR epidemic model is defined and the dynamical behavior of the model is studied. It is proved that the disease free equilibrium is globally asymptotically stable if , and the persistence of the model is obtained when . The main attention is paid to the global stability of the endemic equilibrium. Read More

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http://dx.doi.org/10.1186/1687-1847-2013-42DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7100002PMC
February 2013

Global dynamics for an SIR patchy model with susceptibles dispersal.

Adv Differ Equ 2012 1;2012(1):131. Epub 2012 Aug 1.

School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang, 471003 P.R. China.

An epidemiological model with suscptibles dispersal between two patches is addressed and discussed. The basic reproduction numbers and are defined as the threshold parameters. It shows that if both and are below unity, the disease-free equilibrium is shown to be globally asymptotically stable by using the comparison principle of the cooperative systems. Read More

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http://dx.doi.org/10.1186/1687-1847-2012-131DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7099918PMC
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