Multistability of memristive Cohen-Grossberg neural networks with non-monotonic piecewise linear activation functions and time-varying delays.
The problem of coexistence and dynamical behaviors of multiple equilibrium points is addressed for a class of memristive Cohen-Grossberg neural networks with non-monotonic piecewise linear activation functions and time-varying delays. By virtue of the fixed point theorem, nonsmooth analysis theory and other analytical tools, some sufficient conditions are established to guarantee that such n-dimensional memristive Cohen-Grossberg neural networks can have 5(n) equilibrium points, among which 3(n) equilibrium points are locally exponentially stable. It is shown that greater storage capacity can be achieved by neural networks with the non-monotonic activation functions introduced herein than the ones with Mexican-hat-type activation function. In addition, unlike most existing multistability results of neural networks with monotonic activation functions, those obtained 3(n) locally stable equilibrium points are located both in saturated regions and unsaturated regions. The theoretical findings are verified by an illustrative example with computer simulations.
Department of Mathematics, Southeast University, Nanjing 210096, China; School of Computing, Engineering and Mathematics, University of Western Sydney, Sydney NSW 2751, Australia. Electronic address: xbnie@seu.edu.cn.
Xiaobing
X
Nie
School of Computing, Engineering and Mathematics, University of Western Sydney, Sydney NSW 2751, Australia. Electronic address: w.zheng@uws.edu.au.
Wei Xing
WX
Zheng
Department of Mathematics, Southeast University, Nanjing 210096, China; Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia. Electronic address: jdcao@seu.edu.cn.
Jinde
J
Cao
D000465:Algorithms; D003198:Computer Simulation; D016014:Linear Models; D016571:Neural Networks, Computer
Memristive Cohen–Grossberg neural networks; Multistability; Non-monotonic piecewise linear activation functions; Time-varying delays