共查询到20条相似文献，搜索用时 15 毫秒
1.
Xiaomei Feng Kai Wang Fengqin Zhang Zhidong Teng 《Mathematical Methods in the Applied Sciences》2017,40(7):2762-2771
The global stability of equilibria is investigated for a nonlinear multi‐group epidemic model with latency and relapses described by two distributed delays. The results show that the global dynamics are completely determined by the basic reproduction number under certain reasonable conditions on the nonlinear incidence rate. Moreover, compared with the results in Michael Y. Li and Zhisheng Shuai, Journal Differential Equations 248 (2010) 1–20, it is found that the two distributed delays have no impact on the global behaviour of the model. Our study improves and extends some known results in recent literature. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
2.
A delayed multi‐group SVEIR epidemic model with vaccination and a general incidence function has been formulated and studied in this paper. Mathematical analysis shows that the basic reproduction number plays a key role in the dynamics of the model: the disease‐free equilibrium is globally asymptotically stable when , while the endemic equilibrium exists uniquely and is globally asymptotically stable when . For the proofs, we exploit a graph‐theoretical approach to the method of Lyapunov functionals. Our results show that distributed delay has no impact on the global stability of equilibria, and the results improve and generalize some known results. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
3.
Haitao Song Shengqiang Liu Weihua Jiang 《Mathematical Methods in the Applied Sciences》2017,40(6):2153-2164
In this paper, a multistage susceptible‐infectious‐recovered model with distributed delays and nonlinear incidence rate is investigated, which extends the model considered by Guo et al. [H. Guo, M. Y. Li and Z. Shuai, Global dynamics of a general class of multistage models for infectious diseases, SIAM J. Appl. Math., 72 (2012), 261–279]. Under some appropriate and realistic conditions, the global dynamics is completely determined by the basic reproduction number R0. If R0≤1, then the infection‐free equilibrium is globally asymptotically stable and the disease dies out in all stages. If R0>1, then a unique endemic equilibrium exists, and it is globally asymptotically stable, and hence the disease persists in all stages. The results are proved by utilizing the theory of non‐negative matrices, Lyapunov functionals, and the graph‐theoretical approach. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
4.
本文考虑具有S型分布时滞和脉冲的Cohen-Grossberg神经网络模型,应用Lya-punov函数,M矩阵和Razumikhin技巧,得到了该模型稳定的充分条件. 相似文献
5.
This article considers the problem of consensus for discrete‐time networks of multiagent with time‐varying delays and quantization. It is assumed that the logarithmic quantizer is utilized between the information flow through the sensor of each agent, and its quantization error is included in the proposed method. By constructing a suitable Lyapunov‐Krasovskii functional and utilizing matrix theory, a new consensus criterion for the concerned systems is established in terms of linear matrix inequalities (LMIs) which can be easily solved by various effective optimization algorithms. Based on the consensus criterion, a designing method of consensus protocol is introduced. One numerical example is given to illustrate the effectiveness of the proposed method. © 2014 Wiley Periodicals, Inc. Complexity 21: 163–176, 2015 相似文献
6.
In this paper, the 2D Navier‐Stokes‐Voight equations with 3 delays in is considered. By using the Faedo‐Galerkin method, Lions‐Aubin lemma, and Arzelà‐Ascoli theorem, we establish the global well‐posedness of solutions and the existence of pullback attractors in H1. 相似文献
7.
Gnaneswaran Nagamani Thirunavukkarasu Radhika Pagavathi Balasubramaniam 《Complexity》2016,21(5):248-264
This article presents the robust dissipativity and passivity analysis of neutral‐type neural networks with leakage time‐varying delay via delay decomposition approach. Using delay decomposition technique, new delay‐dependent criteria ensuring the considered system to be ‐γ dissipative are established in terms of strict linear matrix inequalities. A new Lyapunov–Krasovskii functional is constructed by dividing the discrete and neutral delay intervals into m and l segments, respectively, and choosing different Lyapunov functionals to different segments. Further, the dissipativity behaviors of neural networks which are affected due to the sensitiveness of the time delay in the leakage term have been taken into account. Finally, numerical examples are provided to show the effectiveness of the proposed method. © 2015 Wiley Periodicals, Inc. Complexity 21: 248–264, 2016 相似文献
8.
This paper studies an (n+4)-dimensional nonlinear virus dynamics model that characterizes the interactions of the viruses, susceptible host cells, n-stages of infected cells, B cells and cytotoxic T lymphocyte (CTL) cells. Both viral and cellular infections have been incorporated into the model. The infected-susceptible and virus-susceptible infection rates as well as the generation and removal rates of all compartments are described by general nonlinear functions. Five threshold parameters are computed, which insure the existence of the equilibria of the model under consideration. A set of conditions on the general functions has been established, which is sufficient to investigate the global dynamics of the model. The global asymptotic stability of all equilibria is proven by utilizing Lyapunov function and LaSalle's invariance principle. The theoretical results are illustrated by numerical simulations of the model with specific forms of the general functions. 相似文献
9.
《Mathematical Methods in the Applied Sciences》2018,41(5):2095-2104
In this article, we present several results on global exponential stability of a fractional‐order cellular neural network with impulses and with time‐varying and distributed delay. By using the Lyapunov‐like function methods in conjunction with the Razumikhin techniques, we derive sufficient condition for the exponential stability with an exponential convergence rate. The obtained outcomes of our present investigation significantly extend and generalize the corresponding results existing in the current literature. Finally, we give 2 illustrative examples to demonstrate the theoretical findings. 相似文献
10.
Synchronization criteria for coupled neural networks with interval time-varying delays and leakage delay 总被引：3，自引：0，他引：3
M.J. ParkO.M. Kwon Ju H. ParkS.M. Lee E.J. Cha 《Applied mathematics and computation》2012,218(12):6762-6775
This paper considers the synchronization problem for coupled neural networks with interval time-varying delays and leakage delay. By construction of a suitable Lyapunov-Krasovskii’s functional and utilization of Finsler’s lemma, novel delay-dependent criteria for the synchronization of the networks are established in terms of linear matrix inequalities (LMIs) which can be easily solved by various effective optimization algorithms. Two numerical examples are given to illustrate the effectiveness of the proposed methods. 相似文献
11.
Cemil Tun 《Annals of Differential Equations》2012,(1):11-14
This paper considers a kind of seventh order nonlinear differential equations with a deviating argument.By means of the Lyapunov direct method,some sufficient conditions are established to show the instability of the zero solution to the equation.Our result is new and complements the corresponding result of [5]. 相似文献
12.
A. Korobeinikov 《Applied Mathematics Letters》2002,15(8):1333-960
Lyapunov functions for classical SIR, SIRS, and SIS epidemiological models are introduced. Global stability of the endemic equilibrium states of the models is thereby established. 相似文献
13.
《Communications in Nonlinear Science & Numerical Simulation》2014,19(10):3753-3765
In this paper, mathematical analysis is carried out for a multiple infected compartments model for waterborne diseases, such as cholera, giardia, and rotavirus. The model accounts for both person-to-person and water-to-person transmission routes. Global stability of the equilibria is studied. In terms of the basic reproduction number , we prove that, if , then the disease-free equilibrium is globally asymptotically stable and the infection always disappears; whereas if , there exists a unique endemic equilibrium which is globally asymptotically stable for the corresponding fast–slow system. Numerical simulations verify our theoretical results and present that the decay rate of waterborne pathogens has a significant impact on the epidemic growth rate. Also, we observe numerically that the unique endemic equilibrium is globally asymptotically stable for the whole system. This statement indicates that the present method need to be improved by other techniques. 相似文献
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J. H. Park 《Journal of Optimization Theory and Applications》2005,124(2):491-502
In this article, the guaranteed cost control problem for a class of neutral delay systems is investigated. A linear--quadratic cost function is considered as a performance measure for the closed-loop system. Based on the Lyapunov method, delay-dependent criteria, which are expressed in terms of matrix inequalities, are proposed to guarantee the asymptotic stability of the system. The matrix inequalities can be solved easily by various efficient optimization algorithms. 相似文献
17.
Boumedine Chentouf Aissa Guesmia 《Mathematical Methods in the Applied Sciences》2019,42(13):4584-4605
This paper is concerned with the asymptotic behavior analysis of solutions to a multidimensional wave equation. Assuming that there is no displacement term in the system and taking into consideration the presence of distributed or discrete time delay, we show that the solutions exponentially converge to their stationary state. The proof mainly consists in utilizing the resolvent method. The approach adopted in this work is also used to other physical systems. 相似文献
18.
E. Camouzis E. Chatterjee G. Ladas 《Journal of Difference Equations and Applications》2013,19(11):1029-1035
An interpretation of Cull's enveloping method used to determine global asymptotic stability of one dimensional population models is given. This is done by relating the enveloping property with the existence of a global Lyapunov function. Following this spirit we revisit a result of Liz. 相似文献
19.
Baodan Tian Shouming Zhong Ning Chen Xianqing Liu 《Mathematical Methods in the Applied Sciences》2014,37(4):496-507
On the basis of the simplest and deterministic chemostat model, we introduce impulsive input, nutrient recycling, and distributed time‐delay into the model in this paper. By using comparison theorem, Floquet theory, and small amplitude skills in the impulsive differential equation, it proves that if the period of impulsive input is too long and the parameter α of the kernel function in the delay is too small, then there exists a microorganism‐eradication periodic solution that is globally asymptotically stable, and the cultivation of the microorganism fails. On the contrary, if we choose suitable impulsive strategy, such as increasing the concentration of the substrate or enhance the proportion of the concentration of the impulsive input of the substrate at periodic time to that for the microbial growth, then the system could be controlled to be permanent, and the cultivation of the microorganism will be successful. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
20.
The exponential stability problem for impulsive systems subject to double state-dependent delays is studied in this paper, where state-dependent delay (SDD) is involved in both continuous dynamics and discrete dynamics and the boundedness of it with respect to states is prior unknown. According to impulsive control theory, we present some Lyapunov-based sufficient conditions for the exponential stability of the concerned system. It is shown that the stabilizing effect of SDD impulses on an unstable SDD system changes the stability and achieves desired performance. In addition, the destabilizing effect of SDD impulses is also fully considered and the corresponding sufficient conditions are derived, which reveals the fact that a stable SDD system can maintain its performance when it is subject to SDD impulsive disturbance. As an application, the proposed result can be employed to the stability analysis of impulsive genetic regulatory networks (GRNs) with SDD and the corresponding sufficient conditions are proposed in terms of the model transformation technique and the linear matrix inequalities (LMIs) technique. In order to demonstrate the effectiveness and applicability of the derived results, we give two examples including impulsive GRNs with SDD and the impulsive controller design for the nonlinear system with SDD. 相似文献