Mittag-Leffler stability of fractional-order neural networks in the presence of generalized piecewise constant arguments.
Neurodynamic system is an emerging research field. To understand the essential motivational representations of neural activity, neurodynamics is an important question in cognitive system research. This paper is to investigate Mittag-Leffler stability of a class of fractional-order neural networks in the presence of generalized piecewise constant arguments. To identify neural types of computational principles in mathematical and computational analysis, the existence and uniqueness of the solution of neurodynamic system is the first prerequisite. We prove that the existence and uniqueness of the solution of the network holds when some conditions are satisfied. In addition, self-active neurodynamic system demands stable internal dynamical states (equilibria). The main emphasis will be then on several sufficient conditions to guarantee a unique equilibrium point. Furthermore, to provide deeper explanations of neurodynamic process, Mittag-Leffler stability is studied in detail. The established results are based on the theories of fractional differential equation and differential equation with generalized piecewise constant arguments. The derived criteria improve and extend the existing related results.
College of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China; Texas A & M University at Qatar, Doha 5825, Qatar; School of Automation, Huazhong University of Science and Technology, Wuhan 430074, China; Institute for Information and System Science, Xi'an Jiaotong University, Xi'an 710049, China. Electronic address: hbnuwu@yeah.net.
Ailong
A
Wu
College of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China. Electronic address: lliu9308@sina.com.
Ling
L
Liu
Texas A & M University at Qatar, Doha 5825, Qatar. Electronic address: tingwen.huang@qatar.tamu.edu.
Tingwen
T
Huang
School of Automation, Huazhong University of Science and Technology, Wuhan 430074, China. Electronic address: hustzgzeng@gmail.com.
Zhigang
Z
Zeng
D016571:Neural Networks, Computer
Fractional-order systems; Generalized piecewise constant arguments; Mittag-Leffler stability; Neurodynamic systems