title: Multistability of complex-valued neural networks with discontinuous activation functions.
abstract: In this paper, based on the geometrical properties of the discontinuous activation functions and the Brouwer's fixed point theory, the multistability issue is tackled for the complex-valued neural networks with discontinuous activation functions and time-varying delays. To address the network with discontinuous functions, Filippov solution of the system is defined. Through rigorous analysis, several sufficient criteria are obtained to assure the existence of 25nequilibrium points. Among them, 9npoints are locally stable and 16n-9nequilibrium points are unstable. Furthermore, to enlarge the attraction basins of the 9nequilibrium points, some mild conditions are imposed. Finally, one numerical example is provided to illustrate the effectiveness of the obtained results.
authors.affiliation: Department of Mathematics, Southeast University, Nanjing 210096, China. Electronic address: jinlliang@seu.edu.cn.
authors.forename: Jinling
authors.initials: J
authors.lastname: Liang
authors.affiliation: Department of Mathematics, Southeast University, Nanjing 210096, China. Electronic address: gong_wei_qiang@163.com.
authors.forename: Weiqiang
authors.initials: W
authors.lastname: Gong
authors.affiliation: Science Program, Texas A&M University, Doha, Qatar. Electronic address: tingwen.huang@qatar.tamu.edu.
authors.forename: Tingwen
authors.initials: T
authors.lastname: Huang
mesh_terms: D000465:Algorithms; D008962:Models, Theoretical; D016571:Neural Networks, Computer; D013997:Time Factors
keywords: Attraction basin; Complex-valued neural networks; Discontinuous function; Multistability