2013/12/24 by Severino H. da Silva, Severino Horácio da Silva, da Silva, Severino Horácio
Computer Science · Engineering · Mathematics · Physics and Astronomy · #35B41 #45J05 #45M05 #Dynamical Systems (math.DS) #FOS: Mathematics #Model Reduction and Neural Networks #Neural Networks Stability and Synchronization #Stability and Controllability of Differential Equations #math.DS #msc:35B41 #msc:45J05 #msc:45M05
paper · pdf · doi:10.48550/arxiv.1312.6745
arxiv created 2013/12/24 · openalex publication_date 2013/12/24 · arxiv updated 2013/12/25 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
In this work we consider the nonlocal evolution equation (∂ 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 L2(S1), where S1 denotes the unit sphere. We obtain stronger results on existence of global attractors and Lypaunov functional than the already existing in the literature. Furthermore, we prove the result, not yet known in the literature, of lower semicontinuity of global attractors with respect to connectivity function J.