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In this paper, we study the well-posedness and asymptotic stability of a thermoelastic laminated beam with past history. For the system with structural damping, without any restriction on the speeds of wave propagations, we prove the exponential and polynomial stabilities which depend on the behavior of the kernel function of the history term, by using the perturbed energy method. For the system without structural damping, we prove the exponential and polynomial stabilities in case of equal speeds and lack of exponential stability in case of non-equal speeds by using the perturbed energy method and Gearhart–Herbst–Prüss–Huang theorem, respectively. Furthermore, the well-posedness of the system is also obtained by using Lumer–Philips theorem.

This paper studies the practical exponential stability of an impulsive stochastic food chain system with time-varying delays (ISOFCSs). By constructing an auxiliary system equivalent to the original system and comparison theorem, the existence of global positive solutions to the suggested system is discussed. Moreover, we investigate the sufficient conditions for the exponential stability and practical exponential stability of the system, which is given by Razumikhin technique and the Lyapunov method. In addition, when Razumikhin’s condition holds, the exponential stability and practical exponential stability of species are independent of time delay. Finally, numerical simulation finds the validity of the method.

The pth ( $p\\geq 1$ ) moment exponential stability, almost surely exponential stability and stability in distribution for stochastic McKean–Vlasov equation are derived based on some distribution-dependent Lyapunov function techniques.

This paper addresses the stability of stochastic delayed recurrent neural networks (SDRNNs), identifying challenges in existing scalar methods, which suffer from strong assumptions and limited applicability. Three key innovations are introduced: (1) weakening noise perturbation conditions by extending diagonal matrix assumptions to non-negative definite matrices; (2) establishing criteria for both mean-square exponential stability and almost sure exponential stability in the absence of input; (3) directly handling complex structures like time-varying delays through matrix analysis. Compared with prior studies, this approach yields broader stability conclusions under weaker conditions, with numerical simulations validating the theoretical effectiveness.

In this paper we study the well-posedness and the asymptotic stability of a one-dimensional thermoelastic Bresse system, where the heat conduction is given by Cattaneo’s law effective in the shear angle displacements. We establish the well-posedness of the system and prove that the system is exponentially stable depending on the parameters of the system. Furthermore, we show that in general, the system is not exponential stable. In this regards, we prove that the solution decays polynomially.

This work focuses on a class of neutral stochastic functional differential equations with jumps and infinite delay (NSFDEwJI). First, we prove the existence and uniqueness of solution maps to NSFDEwJI using successive construction methods, and provide the exponential estimation of solution maps. Next, we establish the boundedness in p th moment of solution maps by Lyapunov function. Finally, with the aid of the Razumikhin argument, we obtain the exponential stability in p th moment. Based on this, the almost sure exponential stability is derived under a specific condition.

Abstract-This article is devoted to analyze the stability of nonlinear stochastic delayed systems driven by G-Brownian motion. Firstly, we study the existence of global unique solution. Secondly, by using G-Ito formula, G-Lyapunov function, Gronwall's inequality and Borel-Cantelli lemma, we discuss the pth moment exponential stability and almost surely exponential stability of stochastic delayed systems. Finally, we provide an example to verify the results.

In this paper, we study the practical exponential stability of nonlinear nonautonomous differential equations under nonlinear perturbations. By introducing a new method, we obtain some explicit criteria for the practical exponential stability of these equations. Furthermore, several characterizations for the exponential stability of a class of nonlinear differential equations are also presented. The obtained results generalize some existing results in the literature. Applications to neutral networks are investigated. Some examples are given to illustrate the obtained results.

This paper aims to analyze the behavior of the solutions of a stochastic perturbed system with respect to the solutions of the stochastic unperturbed system. To prove our stability results, we have derived a new Gronwall-type inequality instead of the Lyapunov techniques, which makes it easy to apply in practice and it can be considered as a more general tool in some situations. On the one hand, we present sufficient conditions ensuring the global practical uniform exponential stability of SDEs based on Gronwall’s inequalities. On the other hand, we investigate the global practical uniform exponential stability with respect to a part of the variables of the stochastic perturbed system by using generalized Gronwall’s inequalities. It turns out that, the proposed approach gives a better result comparing with the use of a Lyapunov function. A numerical example is presented to illustrate the applicability of our results.

The equivalent relation is established here about the stability of stochastic differential equations with piecewise continuous arguments(SDEPCAs) and that of the one-leg θ method applied to the SDEPCAs. Firstly, the convergence of the one-leg θ method to SDEPCAs under the global Lipschitz condition is proved. Secondly, it is proved that the SDEPCAs are pth(p ∈ (0, 1)) moment exponentially stable if and only if the one-leg θ method is pth moment exponentially stable for some sufficiently small step-size. Thirdly, the corollaries that the pth moment exponential stability of the SDEPCAs (the one-leg θ method) implies the almost sure exponential stability of the SDEPCAs (the one-leg θ method) are given. Finally, numerical simulations are provided to illustrate the theoretical results.