Affiliation:
1. School of Mathematics, Suqian University, Suqian 223800, China
2. School of Mathematics, Chengdu Normal University, Chengdu 611130, China
Abstract
We are concerned in this paper with the stability and bifurcation problems for three-neuron-based bi-directional associative memory neural networks that are involved with time delays in transmission terms and possess Caputo fractional derivatives of non-commensurate orders. For the fractional bi-directional associative memory neural networks that are dealt with in this paper, we view the time delays as the bifurcation parameters. Via a standard contraction mapping argument, we establish the existence and uniqueness of the state trajectories of the investigated fractional bi-directional associative memory neural networks. By utilizing the idea and technique of linearization, we analyze the influence of time delays on the dynamical behavior of the investigated neural networks, as well as establish and prove several stability/bifurcation criteria for the neural networks dealt with in this paper. According to each of our established criteria, the equilibrium states of the investigated fractional bi-directional associative memory neural networks are asymptotically stable when some of the time delays are less than strictly specific positive constants, i.e., when the thresholds or the bifurcation points undergo Hopf bifurcation in the concerned networks at the aforementioned threshold constants. In the meantime, we provide several illustrative examples to numerically and visually validate our stability and bifurcation results. Our stability and bifurcation theoretical results in this paper yield some insights into the cause mechanism of the bifurcation phenomena for some other complex phenomena, and this is extremely helpful for the design of feedback control to attenuate or even to remove such complex phenomena in the dynamics of fractional bi-directional associative memory neural networks with time delays.
Funder
Xichu Talents Foundation of Suqian University
the Guiding Science and Technology Planning Program of Suqian
the Excellent Graduation Design (Thesis) Fostering Program of Suqian University
the Innovation and Entrepreneurship Education Reform Research Program of Suqian University
NSFC
the ‘High Quality Public Course Teaching Reform’ Special Program for colleges and universities of Jiangsu
the Higher Education Reform Research Project of Jiangsu
Higher Education Association of China
Subject
Statistics and Probability,Statistical and Nonlinear Physics,Analysis