New criteria on exponential synchronization and existence of periodic solutions of complex BAM networks with delays

Abstract

In this paper, we study a class of time-delayed BAM neural networks with discontinuous activations. Base on the framework of differential inclusion theory and set-valued analysis, by designing discontinuous feedback controller and using some analytic methods, easily verifiable delay-independent criteria are established to guarantee the existence of periodic solution and global exponential synchronization of the drive-response system. Finally, we give a numerical example to illustrate our theoretical analysis. The obtained results are essentially new and they extend previously known results.

Association of Jensen’s inequality for s-convex function with Csiszár divergence

“…for all ξ i ∈ I and α i ≥ 0 with n i=1 α i = 1. Convex function has wide applications in pure and applied mathematics, physics, and other natural sciences [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]; it has many important and interesting properties [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37] such as monotonicity, continuity, and differentiability. Recently, many generalizations and extensions have been made for the convexity, for example, s-convexity [38], strong convexity [39][40][41], preinvexity [42], GA-convexity [43], GG-convexity [44], Schur convexity [45][46][47][48]…”