Abstract
This paper is concerned with the shunting inhibitory cellular neural networks (SICNNs) with time-varying delays in the leakage (or forgetting) terms. Under proper conditions, we employ a novel argument to establish a criterion on the global exponential stability of almost periodic solutions by using Lyapunov functional method and differential inequality techniques. We also provide numerical simulations to support the theoretical result.
Highlights
1 Introduction It is well known that shunting inhibitory cellular neural networks (SICNNs) have been introduced as new cellular neural networks (CNNs) in Bouzerdout and Pinter in [ – ], which can be described by xij(t) = –aij(t)xij(t)
Nr(i, j) = Ckl : max |k – i|, |l – j| ≤ r, ≤ k ≤ m, ≤ l ≤ n, Nq(i, j) is specified. xij is the activity of the cell Cij, Lij(t) is the external input to Cij, the function aij(t) > represents the passive decay rate of the cell activity, Cikjl(t) and Bkijl(t) are the connection or coupling strength of postsynaptic activity of the cell transmitted to the cell Cij, and the activity functions f (·) and g(·) are continuous functions representing the output or firing rate of the cell Ckl, and τ (t) ≥ corresponds to the transmission delay
SICNNs have been extensively applied in psychophysics, speech, perception, robotics, adaptive pattern recognition, vision, and image processing
Summary
There have been extensive results on the problem of the existence and stability of the equilibrium point, periodic and almost periodic solutions of SICNNs with time-varying delays in the literature. The authors of [ – ] dealt with the existence and stability of equilibrium and periodic solutions for neuron networks model involving leakage delays. To the best of our knowledge, few authors have considered the existence and exponential stability of almost periodic solutions of SICNNs with time-varying delays in the leakage terms. Motivated by the discussions above, in this paper, we consider the following SICNNs with time-varying leakage delays: xij(t) = –aij(t)xij t – ηij(t) –. ). By applying Lyapunov functional method and differential inequality techniques, we derive some new sufficient conditions ensuring the existence, uniqueness and exponential stability of the almost periodic solution for system > , and there exist positive constants η > and λ such that λ < aij(t), eλu Kij(u) du < +∞, and
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
