相关论文: Lyapunov Function Partial Differential Equations f…
In this paper, We study the stability of solutions of fuzzy differential equations by Lyapunov's second method. By using scale equations and comparison principle for Lyapunov - like functions, we give some sufficient criterias for the…
We consider kinetic SDEs with low regularity coefficients in the setting recently introduced in [6]. For the solutions to such equations, we first prove a Harnack inequality. Using the abstract approach of [5], this inequality then allows…
Spectral methods are an important part of scientific computing's arsenal for solving partial differential equations (PDEs). However, their applicability and effectiveness depend crucially on the choice of basis functions used to expand the…
The measured spatiotemporal response of various physical processes is utilized to infer the governing partial differential equations (PDEs). We propose SimultaNeous Basis Function Approximation and Parameter Estimation (SNAPE), a technique…
Lyapunov's indirect method is an attractive method for analyzing stability of non-linear systems since only the stability of the corresponding linearized system needs to be determined. Unfortunately, the proof for finite-dimensional systems…
We characterize stable differential-algebraic equations (DAEs) using a generalized Lyapunov inequality. The solution of this inequality is then used to rewrite stable DAEs as dissipative Hamiltonian (dH) DAEs on the subspace where the…
In this paper nonstandard finite difference (NSFD) schemes of two metapopulation models are constructed. The stability properties of the discrete models are investigated by the use of a generalization of Lyapunov stability theorem. Due to…
We analyze the exponential stability of distributed parameter systems. The system we consider is described by a coupled parabolic partial differential equation with spatially varying coefficients. We approximate the coefficients by…
In this paper, we study a certain class of nonlocal partial differential equations (PDEs). The equations arise from a key problem in network science, i.e., network generation from local interaction rules, which result in a change of the…
This study presents new estimates for fractional derivatives without singular kernels defined by some specific functions. Based on obtained inequalities, we give a useful method to establish the global stability of steady states for…
We analyze stochastic partial differential equations (SPDEs) with quadratic nonlinearities close to a change of stability. To this aim we compute finite-time Lyapunov exponents (FTLEs), observing a change of sign based on the interplay…
This paper proposes a line integral Lyapunov function approach to stability analysis and stabilization for It\^o stochastic T-S models. Unlike the deterministic case, stability analysis of this model needs the information of Hessian matrix…
Quantitative estimates for the top Lyapunov exponents for systems of stochastic reaction-diffusion equations are proven. The treatment includes reaction potentials with degenerate minima. The proof relies on an asymptotic expansion of the…
The article proposes an approach to complete-type and related Lyapunov-Krasovskii functionals that neither requires knowledge of the delay-Lyapunov matrix function nor does it involve linear matrix inequalities. The approach is based on…
We represent an algorithm allowing one to construct new classes of partially integrable multidimensional nonlinear partial differential equations (PDEs) starting with the special type of solutions to the (1+1)-dimensional hierarchy of…
This paper develops the concept of decomposition for chemical reaction networks, based on which a network decomposition technique is proposed to capture the stability of large-scale networks characterized by a high number of species, high…
Partial differential equations (PDEs) underlie our understanding and prediction of natural phenomena across numerous fields, including physics, engineering, and finance. However, solving parametric PDEs is a complex task that necessitates…
Partial differential equations (PDEs) are crucial for modeling various physical phenomena such as heat transfer, fluid flow, and electromagnetic waves. In computer-aided engineering (CAE), the ability to handle fine resolutions and large…
Motivated by the fact that the pseudo-Helmholtz function is a valid Lyapunov function for characterizing asymptotic stability of complex balanced mass action systems (MASs), this paper develops the generalized pseudo-Helmholtz function for…
In this paper, we propose a Lyapunov-based reinforcement learning method for distributed control of nonlinear systems comprising interacting subsystems with guaranteed closed-loop stability. Specifically, we conduct a detailed stability…