共查询到20条相似文献，搜索用时 15 毫秒
1.
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
2.
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
3.
In this paper, the pth moment exponential stability for a class of impulsive stochastic functional differential equations with Markovian switching is investigated. Based on the Lyapunov function, Dynkin formula and Razumikhin technique with stochastic version as well as stochastic analysis theory, many new sufficient conditions are derived to ensure the pth moment exponential stability of the trivial solution. The obtained results show that stochastic functional differential equations with/without Markovian switching may be pth moment exponentially stabilized by impulses. Moreover, our results generalize and improve some results obtained in the literature. Finally, a numerical example and its simulations are given to illustrate the theoretical results. 相似文献
4.
《Journal of The Franklin Institute》2019,356(13):7347-7370
In this paper, we study a stochastic SIR epidemic model with distributed delay and degenerate diffusion. Firstly, we transform the stochastic model into an equivalent system which contains three equations. Since the diffusion matrix is degenerate, the uniform ellipticity condition is not satisfied. The Markov semigroup theory is used to obtain the existence and uniqueness of a stable stationary distribution. We verify the densities of the distributions of the solutions can converge in L1 to an invariant density. Then we establish sufficient conditions for extinction of the disease. Some examples and numerical simulations are introduced to illustrate our analytical results. 相似文献
5.
This paper investigates pth moment boundedness of neutral stochastic functional differential equations with Markovian switching (NSFDEsMS) based on Razumikhin technique and comparison principle. And pth moment stability is examined as a special case. Since the stochastic disturbances and neutral delays are incorporated, the considered system becomes more complex. Besides, the coefficients of the estimated upper bound for the diffusion operation associated with the underlying NSFDEsMS also may be chosen to be sign-changing functions instead of constant functions or negative definite functions, as a result, our results can work in general non-autonomous neutral stochastic systems. Finally, two examples are provided to show the effects of the proposed methods. 相似文献
6.
This paper gives some Razumikhin-type theorems on pth moment boundedness of stochastic functional differential equations with Markovian switching (SFDEwMS) by using Razumikhin technique and comparison principle. Some improved conditions on pth moment stability are also proposed. The main results of this paper allow the estimated upper bound of the diffusion operator associated with the underlying SFDEwMS of the Lyapunov function to have time-varying coefficients (the coefficients may even be sign-changing functions). Examples are provided to illustrate the effectiveness of the proposed results. 相似文献
7.
In this paper we study boundary value problems for anisotropic partial differential-operator equations with parameters. The principal part of the appropriate differential operators are not self-adjoint. Several conditions for the uniform separability in weighted Banach-valued Lp-spaces are given. Sharp estimates for the resolvent of the corresponding differential operator are obtained. In particular the positivity and R-positivity of these operators are established. As an application we study the separability of degenerate DOEs, maximal regularity for degenerate abstract parabolic problem with parameters, the uniform separability of finite and infinite systems for degenerate anisotropic partial differential equations with parameters. 相似文献
8.
Certain inequalities are presented, related to the L2 norms of the solutions to the vibrating string and heat conduction partial differential equations; in particular, an “L2 maximum principle” is derived for the heat equation, and similar inequalities for the vibrating string problem. 相似文献
9.
In this paper, we consider multipoint boundary value problem for third-order differential equations with p-Laplacian at resonance
10.
By means of Mawhin's continuation theorem, we study a third-order p-Laplacian differential equation
(?p(u″(t)))′+f(t,u′(t),u″(t))+g(t,u(t-τ(t)))=e(t). 相似文献
11.
A. Caicedo C. Cuevas G.M. Mophou G.M. N’Guérékata 《Journal of The Franklin Institute》2012,349(1):1-24
We prove in this paper the existence and uniqueness of mild solutions to some functional differential and functional integro-differential equations with infinite delay in Banach spaces which approach almost automorphic functions at infinity. We also discuss the existence of S-asymptotically mild solutions. The results are new. 相似文献
12.
Stability analysis of a class of stochastic differential delay equations with nonlinear impulsive effects 总被引：1，自引：0，他引：1
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.
14.
By means of Mawhin's continuation theorem, we study a kind of fourth-order p-Laplacian neutral functional differential equation with a deviating argument in the form:
(φp(x(t)−cx(t−δ))″)″=f(x(t))x′(t)+g(t,x(t−τ(t,|x|∞)))+e(t). 相似文献
15.
By using the Razumikhin-type technique, for stochastic discrete-time delay systems, this paper establishes the discrete Razumikhin-type theorems on the pth moment stability, the global pth moment stability and the pth moment exponential stability, respectively. The almost sure exponential stability is also investigated by using the pth moment exponential stability and the Borel–Cantelli lemma. As the applications of t he established theorems, stability of a special class of stochastic discrete-time delay systems, synchronization of the stochastic discrete-time delay dynamical networks and stabilization of a stochastic discrete-time linear delay time invariant system are examined. 相似文献
16.
Using Lu's continuation theorem, the extension one of Manásevich-Mawhin, we study the existence of periodic solutions for p-Laplacian neutral Liénard equation of the form
(?p(x(t)-cx(t-σ))′)′+f(x(t))x′(t)+β(t)g(x(t-τ(t))=e(t). 相似文献
17.
《Journal of The Franklin Institute》2022,359(13):6829-6855
In this paper, the linear quadratic (LQ) optimal decentralized control and stabilization problems are investigated for multi-sensors networked control systems (MSNCSs) with multiple controllers of different information structure. Specifically, for a MSNCS, in view of the packet dropouts and the transmission delays, each controller may access different information sets. To begin with, the sufficient and necessary solvability conditions for the LQ decentralized control problems are developed. Consequently, for the purpose of deriving the optimal decentralized control strategy, an innovative orthogonal decomposition method is proposed to decouple the forward and backward stochastic difference equations (FBSDEs) from the maximum principle. In the following, we show that the optimal decentralized controller can be calculated according to a set of Riccati-type equations. Finally, a stabilizing controller is derived for the stabilization problem. 相似文献
18.
This paper is concerned with the input-to-state stability (ISS) of impulsive stochastic systems. First, appropriate concepts of stochastic input-to-state stability (SISS) and pth moment input-to-state stability (p-ISS) for the mentioned systems are introduced. Then, we prove that impulsive stochastic systems possessing SISS-Lyapunov functions are uniformly SISS and p-ISS over a certain class of impulse sequences. As a byproduct, a criterion on the uniform global asymptotic stability in probability for the system in isolation (without inputs) is also derived. Finally, we provide a numerical example to illustrate our results. 相似文献
19.
Baolong Zhu Mingliang Suo Ying Chen Zhiping Zhang Shunli Li 《Journal of The Franklin Institute》2018,355(7):3310-3329
In this paper, we consider the problem of mixed H∞ and passivity control for a class of stochastic nonlinear systems with aperiodic sampling. The system states are unavailable and the measurement is corrupted by noise. We introduce an impulsive observer-based controller, which makes the closed-loop system a stochastic hybrid system that consists of a stochastic nonlinear system and a stochastic impulsive differential system. A time-varying Lyapunov function approach is presented to determine the asymptotic stability of the corresponding closed-loop system in mean-square sense, and simultaneously guarantee a prescribed mixed H∞ and passivity performance. Further, by using matrix transformation techniques, we show that the desired controller parameters can be obtained by solving a convex optimization problem involving linear matrix inequalities (LMIs). Finally, the effectiveness and applicability of the proposed method in practical systems are demonstrated by the simulation studies of a Chua’s circuit and a single-link flexible joint robot. 相似文献
20.
L.W. Blau 《Journal of The Franklin Institute》1928,206(3):355-378
The solution of the differential equation y″ + 2Ry′ + n2y = E cos pt is written in a new form which clearly exhibits many important facts thus far overlooked by theoretical and experimental investigators. Writing s = n ? p, and Δn = n ? √n2 ? R2, it is found: (a) When s ≠ Δn, there are “beats,” and the first “beat” maximum is greater than any later maximum while the first “beat” minimum is less than any later “beat” minimum. The “beat” frequency is . (b) When n2 ? p2 = R2, there are no “beats,” and the resultant amplitude grows monotonically from zero to the amplitude of the forced vibration, (c) At resonance, when n = p, we still have maxima which occur with a frequency in a damped system. (d) The absence of “beats” is neither a sufficient nor a necessary condition for resonance in a damped system.In the experimental investigation the upper extremity of a simple pendulum was moved in simple harmonic motion and photographic records obtained of the motion of the pendulum bob. Different degrees of damping were used, ranging from very small to critical.The experimental results are in excellent agreement with theory. 相似文献