Dynamic behavior of nonautonomous cellular neural networks with time-varying delays

New proof on exponential convergence for cellular neural networks with time-varying delays

“…where g j (x) = f j (x) = 0.03 sin x 2 (j = 1, 2, 3) and a 11 (t) a 12 (t) b11 (t) b 12 (t) = 0.2 + 0.4 sin 4500t 0.2 + 0.3 sin 4500t 0.1 + 0.4 cos 4500t 0.1 + 0.4 cos 4500t , a 21 (t) a 22 (t) b 21 (t) b 22 (t) = 0.1 + 0.4 cos 5000t 0.2 + 0.3 cos 5000t 0.2 + 0.2 cos 5000t 0.1 + 0.4 sin 5000t ,…”

Novel Stability Results for Halanay Inequality and Applications to Delay Neural Networks

“…Remark 11: Obviously, the function a 1 (t) < 0 and a 2 (t) < 0 for t ∈ (2kπ + π 6 , 2kπ + 5π 6 ), k ∈ N, which means that a 1 (t) and a 2 (t) can be negative in some intervals. Therefore the existing works [10], [15], [16] can not be applied to this situation.…”

Nonlinear dynamics of full-range CNNs with time-varying delays and variable coefficients

“…Remark 2. The continuous systems in [19,21,22] and the discontinuous systems in [23,35,39] about GES were studied, but the set-valued term N Q (x(t)) is not introduced into their systems. In [28], the systemẋ(t) ∈ Ax(t) + I − N Q (x(t)) was proposed and studied.…”

“…Remark 5. When we calculate the time derivative of the Lyapunov function in the proof of Theorem 2, system (7) contains set-valued item N Q (x(t)), which leads to the additional difficulty compared with the systems in [19,[21][22][23]. We overcome this difficulty by using the monotonicity of the normal cone and the measurable selection theorem.…”

“…In [19], the GES of CNNs with multi-proportional delays was considered. The more theoretical results on the GES of the CNNs can be found in [1,18,21,23,33,34,38,42].…”