International Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101120171110Hybrid function projective synchronization in discrete dynamical networks via adaptive control55935607http://dx.doi.org/10.22436/jnsa.010.11.01ENGhada Al-mahbashiSchool of mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM, Selangor Darul Ehsan, MalaysiaM. S. Md NooraniSchool of mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM, Selangor Darul Ehsan, MalaysiaSakhinah Abu BakarSchool of mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM, Selangor Darul Ehsan, MalaysiaIn this paper, we study the hybrid function projective synchronization between coupled complex discrete networks with different dimensions.
The hybrid function projective synchronization is achieved by designing an adaptive control method. Based on the designed controller and the Lyapunov stability theory, we derive sufficient conditions to realize the hybrid function projective synchronization with different nodes. Moreover, with the adaptive update law, an adaptive control gains are obtained. Furthermore, we examine different cases of outer coupling matrix of node dynamics. Finally, we provide numerical examples to show the effectiveness of the proposed control scheme.http://www.isr-publications.com/jnsa/6067/download-hybrid-function-projective-synchronization-in-discrete-dynamical-networks-via-adaptive-controlInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101120171110Anti-synchronization of fractional-order chaotic complex systems with unknown parameters via adaptive control56085621http://dx.doi.org/10.22436/jnsa.010.11.02ENCuimei JiangSchool of Science, Qilu University of Technology, Jinan, Shandong 250353, P. R. ChinaFangfang ZhangSchool of Electrical Engineering and Automation, Qilu University of Technology, Jinan, Shandong 250353, P. R. ChinaHaiyong QinSchool of Mathematics, Qilu Normal University, Jinan, Shandong 250013, P. R. ChinaTongxing LiSchool of Information Science and Engineering, Linyi University, Linyi, Shandong 276005, P. R. ChinaThis paper is concerned with adaptive control for anti-synchronization of a class of uncertain fractional-order chaotic complex systems described by a unified mathematical expression.
By utilizing the recently established result for the Caputo fractional derivative of a quadratic function
and employing the adaptive control technique, we design controllers and some fractional-order
parameter update laws
to anti-synchronize two fractional-order chaotic complex systems with unknown parameters.
The proposed method has generality, simplicity, and feasibility.
Moreover, anti-synchronization between uncertain fractional-order complex Lorenz system and fractional-order complex Lu system is implemented as an example to demonstrate the effectiveness and feasibility of the proposed scheme.http://www.isr-publications.com/jnsa/6068/download-anti-synchronization-of-fractional-order-chaotic-complex-systems-with-unknown-parameters-via-adaptive-controlInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101120171110The stochastic interactions between predator and prey under Markovian switching: competitive interaction between multiple prey56225645http://dx.doi.org/10.22436/jnsa.010.11.03ENYanqing LiCollege of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, P. R. ChinaLong ZhangCollege of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, P. R. ChinaIn this paper, a class of
predator-prey model with prey competition is proposed, in which the interactions of predation between predator and prey are randomised and subsequently evaluated under Markovian switching. By constructing appropriate Lyapunov functions and applying various analytical methods, sufficient conditions for the existence of unique global positive solution, stochastic permanence and mean extinction are established. In the permanence case, we also estimate the superior and inferior limits of the sample path in a time-averaged Markov decision. We conclude that the interactions between predator and two prey, two competitive prey themselves and the dynamical properties of switching subsystems are not only dependent on subsystem coefficients but also on the transition probability of the Markov chain (switching from one state to another). Specific examples and numerical simulations are provided to demonstrate our theoretical results.http://www.isr-publications.com/jnsa/6069/download-the-stochastic-interactions-between-predator-and-prey-under-markovian-switching-competitive-interaction-between-multiple-preyInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101120171110Robustness analysis of global exponential stability in neural networks evoked by deviating argument and stochastic disturbance56465667http://dx.doi.org/10.22436/jnsa.010.11.04ENLiguang WanCollege of Mechatronics and Control Engineering, Hubei Normal University, Huangshi 435002, ChinaAilong WuCollege of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, ChinaJingru ChenDepartment of Personnel, Hubei Normal University, Huangshi 435002, ChinaThis paper studies the robustness of global exponential stability of
neural networks evoked by deviating argument and stochastic
disturbance. Given the original neural network is globally
exponentially stable, we discuss the problem that the neural network
is still globally exponentially stable when the deviating argument
or both the deviating argument and stochastic disturbance is/are
generated. By virtue of solving the derived transcendental
equation(s), the upper bound(s) about the intensity of the deviating
argument or both of the deviating argument and stochastic
disturbance is/are received. The obtained theoretical results are
the supplements to the existing literatures on global exponential
stability of neural networks. Two numerical examples are offered to
demonstrate the effectiveness of theoretical results.http://www.isr-publications.com/jnsa/6070/download-robustness-analysis-of-global-exponential-stability-in-neural-networks-evoked-by-deviating-argument-and-stochastic-disturbanceInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101120171110Some fixed point theorems for \(\varphi\)-contractive mappings in fuzzy normed linear spaces56685676http://dx.doi.org/10.22436/jnsa.010.11.05ENSorinNădăbanDepartment of Mathematics and Computer Science, Aurel Vlaicu University of Arad, Elena Dragoi 2, RO-310330, Arad, RomaniaTudorBînzarDepartment of Mathematics, Politehnica University of Timisoara, Regina Maria 1, RO-300004, Timisoara, RomaniaFlavius PaterDepartment of Mathematics, Politehnica University of Timisoara, Regina Maria 1, RO-300004, Timisoara, RomaniaIn this paper a new concept of comparison function is introduced and discussed and some fixed point theorems are established for \(\varphi\)-contractive mappings in fuzzy normed linear spaces. In this way we obtain fuzzy versions of some classical fixed point theorems such as Nemytzki-Edelstein's theorem and Maia's theorem. http://www.isr-publications.com/jnsa/6071/download-some-fixed-point-theorems-for-varphi-contractive-mappings-in-fuzzy-normed-linear-spacesInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101120171110Study on differentiability problems of interval-valued functions56775689http://dx.doi.org/10.22436/jnsa.010.11.06ENYu-E BaoCollege of Mathematics, Inner Mongolia University for Nationalities, Tongliao, Inner Mongolia 028043, P. R. ChinaJin-Jun Li College of Mathematics, Inner Mongolia University for Nationalities, Tongliao, Inner Mongolia 028043, P. R. ChinaEer-Dun BaiCollege of Computer Science and Technology, Inner Mongolia Universities, Tongliao, Inner Mongolia 028043, P. R. ChinaIn this paper, we give the concepts of \(H\)-directional differentiability and \(D\)-directional differentiability of interval-valued functions. Then we discuss the properties of \(H\)-directional differentiable interval-valued functions and \(D\)-directional differentiable interval-valued functions. The necessary and sufficient conditions for the \(H\)-directional differentiability are given together with the sufficient conditions and the necessary and sufficient conditions for \(D\)-directional differentiability of interval-valued functions. Then we discuss the relationship between the two directional differentiability and prove these directional differentiability can be equivalent under a certain conditions.http://www.isr-publications.com/jnsa/6072/download-study-on-differentiability-problems-of-interval-valued-functionsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101120171115Fixed points of weakly compatible mappings satisfying a generalized common limit range property56905700http://dx.doi.org/10.22436/jnsa.010.11.07ENAziz KhanDepartment of Mathematics, University of Peshawar, P. O. Box 25000, Khyber Pakhtunkhwa, PakistanHasib KhanCollege of Engineering, Mechanics and Materials, Hohai University, 210098, Nanjing, P. R. ChinaDumitru BaleanuDepartment of Mathematics, Cankaya University, 06530 Ankara, TurkeyErdal KarapinarDepartment of Mathematics, Atilim University, 06586 Incek, Ankara, TurkeyTahir Saeed KhanDepartment of Mathematics, University of Peshawar, P. O. Box 25000, Khyber Pakhtunkhwa, PakistanIn this paper, we produce new fixed point theorems for \(2n\) self-mappings \(\wp^a_1,\wp^a_2,\ldots,\wp^a_n\), \(\gamma^b_1,\gamma^b_2,\ldots,\gamma^b_n:\mathcal{X}\rightarrow\mathcal{X}\) on a metric space \((\mathcal{X},\rho )\), satisfying a generalized common limit range (CLR) property or CLR\(_{\wp^a_k\gamma^b_l}\) for \(k,l=2,\ldots,n\). Along with the newly introduced property CLR\(_{\wp^a_k\gamma^b_l}\) for \(k,l=2,\ldots,n\) for the \(2n\) self-mappings, we also assume that the pairs \((\wp^a_1,\gamma^b_1),(\wp^a_2,\gamma^b_2),\ldots,(\wp^a_n,\gamma^b_n)\) are weakly compatible. From the main result, we produce three more corollaries as its special cases. These results generalize the work of Sarwar et al. [M. Sarwar, M. Bahadur Zada, I. M. Erhan, Fixed Point Theory Appl., \({\bf 2015}\) (2015), 15 pages] and many others in the available literature. Two examples are also presented for the applications of our new FPTs.http://www.isr-publications.com/jnsa/6096/download-fixed-points-of-weakly-compatible-mappings-satisfying-a-generalized-common-limit-range-propertyInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101120171115Hyers-Ulam stability of nonlinear impulsive Volterra integro-delay dynamic system on time scales57015711http://dx.doi.org/10.22436/jnsa.010.11.08ENAkbar ZadaDepartment of Mathematics, University of Peshawar, Peshawar 25000, PakistanSyed Omar ShahDepartment of Mathematics, University of Peshawar, Peshawar 25000, PakistanYongjin LiDepartment of Mathematics, Sun Yat-sen University, Guangzhou, 510275, P. R. ChinaThis paper proves the Hyers-Ulam stability and Hyers-Ulam-Rassias stability of nonlinear impulsive Volterra integro-delay dynamic system on time scales via a fixed point approach. The uniqueness and existence of the solution of nonlinear impulsive Volterra integro-delay dynamic system is proved with the help of Picard operator. The main tools for proving our results are abstract Gronwall lemma and Banach contraction principle. We also make some assumptions along with Lipschitz condition which make our results appropriate for the approach we are
using.http://www.isr-publications.com/jnsa/6097/download-hyers-ulam-stability-of-nonlinear-impulsive-volterra-integro-delay-dynamic-system-on-time-scalesInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101120171115Viscosity regularization iterative methods and convergence analysis57125722http://dx.doi.org/10.22436/jnsa.010.11.09ENDongfeng LiSchool of Information Engineering, North China University of Water Resources and Electric Power, Zhengzhou 450011, ChinaJuan ZhaoSchool of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou 450011, ChinaIn this paper, a Moudafi's type viscosity regularization iterative method is introduced and investigated for an \(m\)-accretive mapping and a nonexpansive mapping. Strong convergence of the regularization iterative method is obtained in the framework of real uniformly smooth Banach spaces. Some subresults are also provided as applications of the main results.http://www.isr-publications.com/jnsa/6098/download-viscosity-regularization-iterative-methods-and-convergence-analysisInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101120171115Some fixed point theorems for \(\theta\)-\(\phi\) \({C}\)-contractions57235733http://dx.doi.org/10.22436/jnsa.010.11.10ENDingwei ZhengCollege of Mathematics and Information Science, Guangxi University, Nanning, Guangxi, 530004, P. R. ChinaXinhe LiuCollege of Mathematics and Information Science, Guangxi University, Nanning, Guangxi, 530004, P. R. ChinaGengrong ZhangCollege of Mathematics and Computationl Science, Hunan First Normal University, Changsha, Hunan, 410205, P. R. ChinaIn this paper, we introduce the notion of \(\theta\)-\(\phi\) \({C}\)-contraction and establish some fixed point and coupled fixed point theorems for these mappings in the setting of complete metric spaces and ordered metric spaces. The results presented in the paper improve and extend some well-known results. Also, we give an example to illustrate them.http://www.isr-publications.com/jnsa/6099/download-some-fixed-point-theorems-for-theta-phi-c-contractionsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101120171115Solvability of second-order \(m\)-point difference equation boundary value problems on infinite intervals57345743http://dx.doi.org/10.22436/jnsa.010.11.11ENChanglong YuCollege of Sciences, Hebei University of Science and Technology, Shijiazhuang, 050018, Hebei, P. R. ChinaJufang WangCollege of Sciences, Hebei University of Science and Technology, Shijiazhuang, 050018, Hebei, P. R. ChinaYanping GuoCollege of Sciences, Hebei University of Science and Technology, Shijiazhuang, 050018, Hebei, P. R. ChinaSurong MiaoCollege of Sciences, Hebei University of Science and Technology, Shijiazhuang, 050018, Hebei, P. R. ChinaIn this paper, we study second-order \(m\)-point
difference boundary value problems on infinite intervals
\[
\left\{\begin{array}{l}
\Delta^{2}x(k-1)+f(k,x(k),\Delta x(k-1))=0,~k\in N,\\
x(0)=\sum\limits_{i=1}^{m-2}\alpha_{i}x(\eta_{i}),~\lim\limits_{k
\rightarrow\infty }\Delta x(k)=0,
\end{array}
\right.
\]
where \(N=\{1,2,\cdots\},\ f:N\times R^{2}\rightarrow R\)
is continuous, \(\alpha_{i}\in
R,~\sum\limits_{i=1}^{m-2}\alpha_{i}\neq1,~\eta_{i}\in
N,~0<\eta_{1}<\eta_{2}<\cdots<\infty\) and
\[\Delta x(k)=x(k+1)-x(k),\]
the nonlinear term is dependent in a difference of lower order on
infinite intervals. By using Leray-Schauder continuation theorem,
the existence of solutions are investigated. Finally, we give one
example to demonstrate the use of the main result. http://www.isr-publications.com/jnsa/6100/download-solvability-of-second-order-m-point-difference-equation-boundary-value-problems-on-infinite-intervalsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101120171115Existence of solutions for nonlinear Caputo-Hadamard fractional differential equations via the method of upper and lower solutions57445752http://dx.doi.org/10.22436/jnsa.010.11.12ENYunru BaiInstitute of Computer Science, Faculty of Mathematics and Computer Science, Jagiellonian University, ul. Lojasiewicza 6, 30-348 Krakow, PolandHua KongData Recovery Key Laboratory of Sichuan Province, College of Mathematics and Information Science, Neijiang Normal University, Neijiang 641100, ChinaThe purpose of this paper is devoted to consider the existence of solutions for a class of nonlinear Caputo-Hadamard fractional differential equations with integral terms ((CHFDE), for short). Firstly, by applying the semi-group property of Hadamard fractional integral operator, a necessary condition of solvability for (CHFDE) is established. Then, under the suitable conditions, we prove the solution set of (CHFDE) is nonempty by using the method of upper and lower solutions, and Arzel\`{a}-Ascoli theorem. Finally, we present several numerical examples to explicate
the main results. http://www.isr-publications.com/jnsa/6101/download-existence-of-solutions-for-nonlinear-caputo-hadamard-fractional-differential-equations-via-the-method-of-upper-and-lower-solutionsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101120171115Dynamics of a diffusive viral model with Beddington-DeAngelis incidence rate and CTL immune response57535762http://dx.doi.org/10.22436/jnsa.010.11.13ENKejun ZhuangSchool of Statistics and Applied Mathematics, Anhui University of Finance and Economics, Bengbu 233030, ChinaIn this paper, a four-dimensional system of viral model with cytotoxic lymphocyte (CTL) immune response is investigated. This model is a reaction-diffusion system with
Beddington-DeAngelis incidence rate and free diffusion in a bounded domain. With the help of comparison principle and Lyapunov function method, the well-posedness of solutions and sufficient conditions for global stability of nonnegative equilibria are established. It can be found that free diffusion has no influence on the global stability of the system with homogeneous Neumann boundary conditions.http://www.isr-publications.com/jnsa/6102/download-dynamics-of-a-diffusive-viral-model-with-beddington-deangelis-incidence-rate-and-ctl-immune-responseInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101120171115Fixed point theorems in fuzzy cone metric spaces57635769http://dx.doi.org/10.22436/jnsa.010.11.14ENSaif Ur RehmanDepartment of Mathematics, Sichuan University, Chengdu, Sichuan 610064, P. R. ChinaHong-Xu LiDepartment of Mathematics, Sichuan University, Chengdu, Sichuan 610064, P. R. ChinaIn this paper we prove some fixed point theorems in fuzzy cone metric spaces under some fuzzy cone contractive type conditions. Our results generalize the ``fuzzy cone Banach contraction theorem'' given by [T. Oner, M. B. Kandemire, B. Tanay, J. Nonlinear Sci. Appl., \(\textbf{8}\) (2015), 610--616] recently. http://www.isr-publications.com/jnsa/6103/download-fixed-point-theorems-in-fuzzy-cone-metric-spacesInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101120171115Weighted Simpson type inequalities for \(h\)-convex functions57705780http://dx.doi.org/10.22436/jnsa.010.11.15ENMarian MatłokaDepartment of Applied Mathematics, Poznań University of Economics, Aleja Niepodległości 10, 61-875 Poznań, PolandIn this paper we establish some weighted Simpson type inequalities
for functions whose derivatives in absolute value are \(h\)-convex.http://www.isr-publications.com/jnsa/6104/download-weighted-simpson-type-inequalities-for-h-convex-functionsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101120171115The necessary and sufficient conditions of Hyers-Ulam stability for a class of parabolic equation57815788http://dx.doi.org/10.22436/jnsa.010.11.16ENXiangkui ZhaoSchool of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, ChinaXiaojun WuSchool of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, ChinaZhihong ZhaoSchool of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, ChinaThe aim of this paper is to consider the Hyers-Ulam stability of a class of parabolic equation \[\left\{\begin{array}{ll}
\frac{\partial u}{\partial t}- a^{2}\Delta u+b\cdot\nabla u+cu=0,~~~(x,t)\in\mathbb{R}^{n}\times(0,+\infty),\\
u(x,0)=\varphi(x),~~~x\in\mathbb{R}^{n}.\end{array}\right.\] We conclude that
(i) it is Hyers-Ulam stable on any finite interval;
(ii) if $c\neq0 $, it is Hyers-Ulam stable on the semi-infinite interval;
(iii) if $c=0$, it is not Hyers-Ulam stable on the semi-infinite interval by using Fourier transformation.
Furthermore, our results can be applied to the mean square Hyers-Ulam stability of parabolic equations driven by an \(n\)-dimensional Brownian motion. http://www.isr-publications.com/jnsa/6107/download-the-necessary-and-sufficient-conditions-of-hyers-ulam-stability-for-a-class-of-parabolic-equationInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101120171115Inequalities via generalized \(\log m\)-convex functions57895802http://dx.doi.org/10.22436/jnsa.010.11.17ENMuhammad Aslam NoorDepartment of Mathematics, COMSATS Institute of Information Technology, Islamabad, PakistanKhalida Inayat NoorDepartment of Mathematics, COMSATS Institute of Information Technology, Islamabad, PakistanFarhat SafdarDepartment of Mathematics, COMSATS Institute of Information Technology, Islamabad, PakistanMuhammad Uzair AwanDepartment of Mathematics, Government College University, Faisalabad, PakistanSaleem UllahDepartment of Mathematics, University of Islamabad, Islamabad, PakistanThe main objective of this paper is to introduce and investigate a new class of
convex functions, which is called as generalized \(\log\)
\(m\)-convex function. Some new Hermite-Hadamard type of integral inequalities
via generalized \(\log\) \(m\)-convex functions are obtained.
Several special cases are also discussed.http://www.isr-publications.com/jnsa/6108/download-inequalities-via-generalized-log-m-convex-functionsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101120171117Approximation with modified Phillips operators58035812http://dx.doi.org/10.22436/jnsa.010.11.18ENDanyal SoybaşDepartment of Mathematics Education, Faculty of Education, Erciyes University, Kayseri 38039, TurkeyIn the present paper, we study modified Phillips operators in simultaneous approximation. The operators discussed here are important as they have link with the well-known Szász operators. We estimate some direct results for the operators.http://www.isr-publications.com/jnsa/6127/download-approximation-with-modified-phillips-operatorsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101120171117Asymptotic behavior of solutions to a class of coupled semilinear parabolic systems with gradient terms58135824http://dx.doi.org/10.22436/jnsa.010.11.19ENYang NaSchool of Mathematics, Jilin University, Changchun 130012, P. R. ChinaYuanyuan NieSchool of Mathematics, Jilin University, Changchun 130012, P. R. ChinaXu ZhouCollege of Computer Science and Technology, Jilin University, Changchun 130012, P. R. ChinaThis paper concerns the asymptotic behavior of solutions
to the Cauchy problem of a class of coupled semilinear parabolic systems with gradient terms.
Using the energy comparison method and comparison principle,
the blow-up theorem of Fujita type is established
and the critical Fujita curve is formulated by spacial dimension,
the behavior of the coefficient of the gradient term at infinity.http://www.isr-publications.com/jnsa/6128/download-asymptotic-behavior-of-solutions-to-a-class-of-coupled-semilinear-parabolic-systems-with-gradient-termsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101120171117Robust weighted expected residual minimization formulation for stochastic vector variational inequalities58255833http://dx.doi.org/10.22436/jnsa.010.11.20ENYong ZhaoCollege of Mathematics and Statistics, Chongqing JiaoTong University, Chongqing 400074, ChinaZai Yun PengCollege of Mathematics and Statistics, Chongqing JiaoTong University, Chongqing 400074, ChinaYun Bin ZhaoSchool of Mathematics, University of Birmingham, Birmingham, UKIn order to deal with (stochastic) multi-objective optimization problems, a robust Pareto optimal solution by minimizing the worst case weighted sum of
objectives on a given weight set is considered [J. Hu, S. Mehrotra, Oper. Res., \(\textbf{60}\) (2011), 936--953], [J. Hu, T. Homem-de-Mello, S. Mehrotra, Manuscript, (2010)]. Based on this idea, we introduce a new class of deterministic model for stochastic vector variational inequalities, called robust weighted expected residual minimization model. Then we propose sample average approximation (SAA) approach to solve robust weighted expected residual minimization problems. Some convergence results are established for the approximation
problem in terms of the optimal value and the set of optimal solutions. http://www.isr-publications.com/jnsa/6129/download-robust-weighted-expected-residual-minimization-formulation-for-stochastic-vector-variational-inequalitiesInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101120171117Stability analysis for a delayed SIR model with a nonlinear incidence rate58345845http://dx.doi.org/10.22436/jnsa.010.11.21ENLuju LiuSchool of Mathematics and Statistics, Henan University of Science and Technology, Luoyang, 471023, ChinaYan WangCollege of Science, China University of Petroleum, Qingdao, 266580, ChinaWe develop an SIR vector-bone epidemic model incorporating
incubation time delay and the nonlinear incidence rate, where the
growth of susceptibles is governed by the logistic equation. The
threshold parameter \(R_0\) is used to determine whether the disease
persists in the population. The model always has the trivial
equilibrium and the disease-free equilibrium whereas admits the
endemic equilibrium if \(R_0\) exceeds one. The disease-free
equilibrium is globally asymptotically stable if \(R_0\) is less than
one, while the system is persistent if \(R_0\) is greater than one.
Furthermore, by applying the time delay as a bifurcation parameter,
the local stability of the endemic equilibrium is discussed and it
loses stability and Hopf bifurcation occurs as the length of the
time delay increases past \(\tau_0\) under certain conditions. An
example is carried out to illustrate the main results.http://www.isr-publications.com/jnsa/6130/download-stability-analysis-for-a-delayed-sir-model-with-a-nonlinear-incidence-rate