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1.
本文利用锥理论和不动点指数定理,研究了一类具状态依赖时滞的脉冲微分方程的正周期解,获得了关于正周期解存在性的若干新的结果。  相似文献   

2.
In this letter, the existence and the global exponential stability of piecewise pseudo almost periodic solutions (PAPT) for bidirectional associative memory neural networks (BAMNNs) with time-varying delay in leakage (or forgetting) terms and impulsive are investigated by applying contraction mapping fixed point theorem, the exponential dichotomy of linear differential equations and differential inequality techniques. Furthermore, we give an explanatory example to illustrate the efficiency of the theoretical predictions.  相似文献   

3.
In this paper, we investigate an eco-epidemic model with distributed time delay and impulsive control strategy. Firstly, by using Floquet theory of impulsive differential equation, we get the condition for the local stability of the prey eradication periodic solutions. Secondly, by means of impulsive equation compare theory, we get the condition for the global asymptotical stability of the prey eradication periodic solutions. Finally we study the permanence of the system. Numerical simulations (bifurcation diagram, the largest Lyapunov exponents and power spectra) are carried out to illustrate the above theoretical analysis and the rich dynamics phenomenon, which are caused by impulsive effects and time delay, for example bifurcation, double period solution, etc.  相似文献   

4.
In this paper, the discrete-time fuzzy cellular neural network with variable delays and impulses is considered. Based on M-matrix theory and analytic methods, several simple sufficient conditions checking the global exponential stability and the existence of periodic solutions are obtained for the neural networks. Moreover, the estimation for exponential convergence rate index is proposed. The obtained results show that the stability and periodic solutions still remain under certain impulsive perturbations for the neural network with stable equilibrium point and periodic solutions. Some examples with simulations are given to show the effectiveness of the obtained results.  相似文献   

5.
In this paper, we consider an initial value problem for linear matrix coefficient systems of the fractional-order neutral differential equations with two incommensurate constant delays in Caputo’s sense. Firstly, we introduce the exact analytical representation of solutions to linear homogeneous and non-homogeneous neutral fractional-order differential-difference equations system by means of newly defined delayed Mittag–Leffler type matrix functions. Secondly, a criterion on the positivity of a class of fractional-order linear homogeneous time-delay systems has been proposed. Furthermore, we prove the global existence and uniqueness of solutions to non-linear fractional neutral delay differential equations system using the contraction mapping principle in a weighted space of continuous functions with regard to classical Mittag–Leffler functions. In addition, Ulam–Hyers stability results of solutions are attained based on fixed-point approach. Finally, we present an example to demonstrate the applicability of our theoretical results.  相似文献   

6.
An impulsive reaction-diffusion periodic food-chain system with Holling type III functional response is presented and studied in this paper. Sufficient conditions for the ultimate boundedness and permanence of the food-chain system are established based on the upper and lower solution method and comparison theory of differential equation. By constructing appropriate auxiliary function, the conditions for the existence of a unique globally stable positive periodic solution are also obtained. Some numerical examples are shown to illustrate our results. A discussion is given in the end of the paper.  相似文献   

7.
研究具有脉冲出生、脉冲接种和时滞的SEIRS传染病模型,分析无病周期解的存在性和全局稳定性,以及传染病模型的持久性,分析控制传染病传播的主要因素。  相似文献   

8.
The periodic differential equation (1+ε cos t)y&#x030B; + py = 0, hereby termed the Carson–Cambi equation, is the simplest second-order differential equation having a periodic coefficient associated with the second derivative. Provided |ε|<1, which is the case we examine, then the differential equation is a Hill's equation and thus possesses regions of stability and instability in the p–ε plane. Ordinary perturbation theory is employed to obtain the stable (periodic) solutions to ε3. Two-timing theory is employed to obtain solutions for values of k near the critical points k = ±12, ±32, ±52. Three-timing is employed to extend the solution near k = ±12. The solutions of the Carson–Cambi equation are compared with the solutions of the corresponding Mathieu equation.  相似文献   

9.
In this paper, on the basis of the theories and methods of ecology and ordinary differential equation, an ecological model consisting of two preys and one predator with impulsive control strategy and seasonal effects is established. Conditions which guarantee the global asymptotical stability of the prey-eradication periodic solution are obtained using the theory of impulsive equations, small amplitude perturbation skills, and comparison techniques. Further, the influences of the impulsive perturbation and seasonal effects on the inherent oscillation are studied numerically. These show to be consistent with the theoretical analysis and rich complex population dynamics, such as species extinction and permanence. Moreover, the population dynamical behavior of the model is demonstrated by the computed largest Lyapunov exponent. By investigating the strange attractors through their computed Fourier spectra, we know that seasonality has a profound effect on the population dynamical behavior. All these results are expected to be of use in the study of dynamic complexity of ecosystems.  相似文献   

10.
We use critical point theory and variational methods to investigate the solutions of a Dirichlet boundary value problem for damped nonlinear impulsive differential equations. The conditions for the existence of solution are established.  相似文献   

11.
In this paper, the asymptotic behavior of a generalized Solow model with endogenous labor growth and impulsive perturbations at fixed moments of time is studied. By using the Lyapunov–Razumikhin method sufficient conditions for week uniform asymptotic stability of the solutions are obtained. We also show that the role of impulses in control the behavior of solutions of impulsive models is very important.  相似文献   

12.
In this paper, we study stability of a class of stochastic differential delay equations with nonlinear impulsive effects. First, we establish the equivalent relation between the stability of this class of stochastic differential delay equations with impulsive effects and that of a corresponding stochastic differential delay equations without impulses. Then, some sufficient conditions ensuring various stabilities of the stochastic differential delay equations with impulsive effects are obtained. Finally, two examples are also discussed to illustrate the efficiency of the obtained results.  相似文献   

13.
This work aims to analyze the exponential stability of a non-linear impulsive neutral stochastic delay differential system. In this study, impulse perturbation is considered a delay-dependent state variable. The solution of the delay-dependent impulsive neutral stochastic delay differential system is associated with the solution of the system without impulses. First, we developed a relation connecting the solution of the neutral stochastic delay differential system without impulses and the solution of the corresponding system with impulses. Then, the conditions of the exponential stability of the proposed impulsive system are derived by determining the stability analysis of the respective system without impulse. The numerical approach for the neutral stochastic delay system without impulses is generated using the Euler-Maruyama method and adopted for the corresponding impulsive system. Finally, the achieved theoretical results are illustrated for applying the Malthusian single species neutral stochastic delay population model with immigration impulses.  相似文献   

14.
In this work, impulsive stabilization problems of discrete-time switched linear systems with time-varying delays are studied. The sequence of impulsive instants is nearly-periodic, i.e., it is close to a periodic impulse and the distance between them is an uncertain bounded term. A time-varying Lyapunov function is introduced to characterize the information of delays, switching signals and impulses, and a stability criterion LMI-based is obtained without any restrictions on the stability of the subsystems. Several design schemes of reduced-order/full-order impulsive controllers with or without time-varying delays are developed. Finally, three numerical examples are provided to illustrate the effectiveness of the established results.  相似文献   

15.
This article investigates the fixed time synchronization (FXTSY) problem of time-varying delayed impulsive inertial neural networks (INNs) with discontinuous activation functions. First, the addressed delayed discontinuous INNs are converted into a first-order differential equation using a generalized variable transformation with suitable tunable variables. Due to the existence of the discontinuities, the delayed discontinuous differential equations are transformed into the differential inclusions by using the differential inclusion theory and set-valued map concepts. Furthermore, by designing the suitable centralized impulsive control and discontinuous control, constructing the novel indefinite type Lyapunov functionals, new algebraic conditions are derived to realize the FXTSY for the leader-following impulsive INNs. Moreover, the settling time is explicitly calculated. Finally, the developed theoretical results are verified by two numerical simulation results.  相似文献   

16.
This paper investigates the pth moment exponential stability of impulsive stochastic functional differential equations. Some sufficient conditions are obtained to ensure the pth moment exponential stability of the equilibrium solution by the Razumikhin method and Lyapunov functions. Based on these results, we further discuss the pth moment exponential stability of generalized impulsive delay stochastic differential equations and stochastic Hopfield neural networks with multiple time-varying delays from the impulsive control point of view. The results derived in this paper improve and generalize some recent works reported in the literature. Moreover, we see that impulses do contribute to the stability of stochastic functional differential equations. Finally, two numerical examples are provided to demonstrate the efficiency of the results obtained.  相似文献   

17.
This paper introduces an efficient direct approach for solving delay fractional optimal control problems. The concepts of the fractional integral and the fractional derivative are considered in the Riemann–Liouville sense and the Caputo sense, respectively. The suggested framework is based on a hybrid of block-pulse functions and orthonormal Taylor polynomials. The convergence of the proposed hybrid functions with respect to the L2-norm is demonstrated. The operational matrix of fractional integration associated with the hybrid functions is constructed by using the Laplace transform method. The problem under consideration is transformed into a mathematical programming one. The method of Lagrange multipliers is then implemented for solving the resulting optimization problem. The performance and computational efficiency of the developed numerical scheme are assessed through various types of delay fractional optimal control problems. Our numerical findings are compared with either exact solutions or the existing results in the literature.  相似文献   

18.
In this paper, the Bagley-Torvik equation, which has an important role in fractional calculus, is solved by generalizing the Taylor collocation method. The proposed method has a new algorithm for solving fractional differential equations. This new method has many advantages over variety of numerical approximations for solving fractional differential equations. To assess the effectiveness and preciseness of the method, results are compared with other numerical approaches. Since the Bagley-Torvik equation represents a general form of the fractional problems, its solution can give many ideas about the solution of similar problems in fractional differential equations.  相似文献   

19.
The topic of the paper is both the pth moment and almost sure stability on a general decay rate for neutral stochastic functional differential equations, by applying the Razumikhin approach. This concept is extended to neutral stochastic differential delay equations. The results obtained in the paper are more general and they may be specialized on the exponential, polynomial or logarithmic stability. Moreover, some neutral stochastic functional differential equations which are not pth moment or almost surely exponentially stable, could be stable with respect to a certain lower decay rate. In that sense, some nontrivial examples are presented to justify and illustrate the usefulness of the theory. More precisely, one can say anything about both the pth moment and almost sure exponential stability, although the solutions are pth moment and almost surely polynomially or logarithmically stable.  相似文献   

20.
The property of input-to-state stability (ISS) of inertial memristor-based neural networks with impulsive effects is studied. Firstly, according to the characteristics of memristor and inertial neural networks, the inertial memristor-based neural networks are built. Secondly, based on the impulsive control theory, the average impulsive interval approach, Halanay differential inequality, Lyapunov method and comparison property, some sufficient conditions ensuring ISS of the inertial memristor-based neural networks under impulsive controller are derived. In this paper, we consider two types of impulse, stabilizing impulses and destabilizing impulses. When the inertial memristor-based neural networks are originally not ISS, by choosing a suitable lower bound of the average impulsive interval, the stabilizing impulses can be used to stabilize the inertial memristor-based neural networks. On the contrary, the inertial memristor-based neural networks are originally ISS, by restricting the upper bound of the average impulsive interval, the ISS of inertial memristor-based neural networks with destabilizing impulses can be ensured. Finally, numerical results are presented to illustrate the main results.  相似文献   

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