Lower Semicontinuity of Global Attractors for a Class of Evolution Equations of Neural Fields Type in a Bounded Domain
Sign Up to like & getrecommendations! Published in 2018 at "Differential Equations and Dynamical Systems"
DOI: 10.1007/s12591-015-0258-6
Abstract: In this work we consider the nonlocal evolution equation $$\displaystyle \frac{\partial u(w,t)}{\partial t}=-u(w,t)+ \int _{S^{1}}J(wz^{-1})f(u(z,t))\mathrm{d}z+ h, \quad h > 0,$$∂u(w,t)∂t=-u(w,t)+∫S1J(wz-1)f(u(z,t))dz+h,h>0,which arises in models of neuronal activity, in $$L^{2}(S^{1})$$L2(S1), where $$S^{1}$$S1 denotes the unit sphere. We… read more here.
Keywords: evolution; global attractors; semicontinuity global; attractors class ... See more keywords
Converging outer approximations to global attractors using semidefinite programming
Sign Up to like & getrecommendations! Published in 2021 at "Automatica"
DOI: 10.1016/j.automatica.2021.109900
Abstract: This paper develops a method for obtaining guaranteed outer approximations for global attractors of continuous and discrete time nonlinear dynamical systems. The method is based on a hierarchy of semidefinite programming problems of increasing size… read more here.
Keywords: semidefinite programming; global attractor; global attractors; outer approximations ... See more keywords