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This paper aims to study an HIV model with age structure and latently in a spatially homogeneous environment. By applying the fixed point theorem, we obtain the existence of the global solution and the global attractor for the model. We also identify the explicit formula of the basic reproduction number by the mean of the Laplace transformation, and confirm that this number predicts whether the infection occurs or not. Through analyzing the root distribution of the characteristic equation, the local stability of the equilibrium is obtained. By appealing to the appropriate Lyapunov functionals, we further study the global stability of the equilibrium. Numerical simulations also validate our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the global asymptotic stability and global exponential stability with respect to the Clifford-valued neutral-type neural network (NN) models with time delays. By considering the neutral term, a Clifford-valued NN model with time delays is formulated, which encompasses real-valued, complex-valued, and quaternion-valued NN models as special cases. In order to achieve our main results, the n -dimensional Clifford-valued NN model is decomposed into 2 m n -dimensional real-valued models. Moreover, a proper function is constructed to handle the neutral term and prove that the equilibrium point exists. Utilizing the homeomorphism theory, linear matrix inequality as well as Lyapunov functional methods, we derive the sufficient conditions corresponding to the existence, uniqueness, and global asymptotic stability with respect to the equilibrium point of the Clifford-valued neutral-type NN model. Numerical examples to demonstrate the effectiveness of the results are provided, and the simulations results are analyzed and discussed. [ABSTRACT FROM AUTHOR]

In this paper, we derive delay and fractional-order dependent sufficient conditions for fractional-order gene regulatory networks (FOGRNs) with time-varying delays to be stable with H ∞ /passivity performance. Distinct from the existing works on delayed FOGRNs, the Lyapunov-Krasovskii functional (LKF) is suitably structured so that the delay functions can be non-differentiable or even have jump type discontinuities. Further, the positive-definiteness condition is relaxed for the matrices involved in LKF. A new set of linear matrix inequality (LMI) conditions that ensure the stability of FOGRNs with certain H ∞ /passivity performance level is derived using various results on fractional derivatives/integrals and convex property of LMIs. Finally, the results obtained are verified with existing FOGRNs via numerical simulations. [ABSTRACT FROM AUTHOR]

In the paper a Lyapunov matrices approach to the parametric optimization problem of a neutral system with two delays and with a P-controller is presented. The value of integral quadratic performance index of quality is equal to the value of Lyapunov functional for the initial function of the neutral system with two delays. The Lyapunov functional is determined by means of the Lyapunov matrix. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the global dynamics of a two-strain flu model with delay. Using the method of Lyapunov functional, we show that if the basic reproduction number is less than one, then both strains die out; but when the number is larger than one, one or both of the strains become endemic. The main results are confirmed by some numerical simulations. The theoretical results obtained here provide some useful information on the impact of the vaccination rate of a single vaccine for one strain on the dynamics of the two strains. [ABSTRACT FROM AUTHOR]

HIV can infect different cell populations such as CD4+ T cells and macrophages. In this paper, we study the global property of the solution of an HIV model with two target cell populations. The model includes general nonlinear rates of viral infection and cell death. For each class of target cells, the time delay between viral entry into cells and viral production is included in the model. We obtain the basic reproductive number of the model, which is shown to provide a threshold condition determining the long-term behavior of the solution of the model. Specifically, we show that the infection-free equilibrium is globally asymptotically stable when the basic reproductive number is less than or equal to 1, and that the infected equilibrium is globally asymptotically stable when the basic reproductive number is greater than 1. We also extend the model with two target cell populations to a general model with n populations. Similar global properties are obtained for the general model. Numerical simulations are performed to illustrate the stability results and to evaluate the relative contribution to viral production from the two cell populations. [ABSTRACT FROM AUTHOR]

In this paper a Lyapunov functional determination method for a linear neutral system with both lumped and distributed time delay is formulated and solved. A form of a Lyapunov functional is assumed and a computing method of its coefficients is given. The Lyapunov functional is constructed for a given time derivative which is calculated on a trajectory of a neutral system with both lumped and distributed time delay. The presented method gives analytical formulas for the Lyapunov functional coefficients. An example illustrating the application of discussed theory is presented. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we investigate the dynamical behavior of a virus infection model with general incidence rate and humoral immunity. By using suitable Lyapunov functional and the LaSalle's invariance principle, we establish the global stability of the three equilibria. The uninfected equilibrium E 0 is globally asymptotically stable if R 0 ≤1, the infected equilibrium without immunity E 1 is globally asymptotically stable if R 1 ≤1 and R 0 >1, the infected equilibrium with humoral immunity E 2 is globally asymptotically stable if R 1 >1. We check our theorems with numerical simulation in the end. [Copyright &y& Elsevier]

Abstract: This paper is concerned with analysis problem for the global exponential stability of the Cohen–Grossberg neural networks with discrete delays and with distributed delays. We first prove the existence and uniqueness of the equilibrium point under mild conditions, assuming neither differentiability nor strict monotonicity for the activation function. Then, we employ Lyapunov functions to establish some sufficient conditions ensuring global exponential stability of equilibria for the Cohen–Grossberg neural networks with discrete delays and with distributed delays. Our results are not only presented in terms of system parameters and can be easily verified and also less restrictive than previously known criteria. A comparison between our results and the previous results admits that our results establish a new set of stability criteria for delayed neural networks. [Copyright &y& Elsevier]

Abstract: Employing Brouwer’s fixed point theorem, matrix theory, a continuation theorem of the coincidence degree and inequality analysis, the authors study further global exponential stability and the existence of periodic solutions of a class of cellular neural networks with delays (DCNNs) in this paper. A family of sufficient conditions is given for checking global exponential stability and the existence of periodic solutions of DCNNs. The results extend and improve the earlier publications. [Copyright &y& Elsevier]