Consider cellular neural networks (CNNs) with time-varying coefficients and delays:
The system can be transformed into the following vector form:
where t ∈ R+ = [0, ∞), and x(t) = (x1(t), x2 t),...,xn(t))T, C(t) = diag(c1(t),c2(t),...,cn(t)), A(t) = (aij(t))n × n, B(t) (bij(t))n × n, f(x(t)) = (f1(x1(t)),f2(x2(t)),...,fn(xn(t)))T, g(x(t-&tgr;(t))) = (g1(x1(t-&tgr;1(t))), g2(x2(t-&tgr;2 (t))),...,gn(xn(t-&tgr;n(t))))T, and I(t) = (I1(t),I2(t),...,In(t))T.
The authors do not require any equilibrium point, and do not require that all nonlinear response functions fi(u) and gi(u) in system 2 be bounded on R+.
Previously, Arik [1], Arik and Tavsanoglu [2], Cao [3], Lu [4], and a number of other researchers obtained many important results for delayed autonomous CNNs, including the existence of equilibrium points, global asymptotic stability, global exponential stability, and bifurcation. These authors applied the technique of matrix analysis, and Liapunov functions were used to address the global exponential stability of the equilibrium point. A number of corollaries, remarks, and two interesting examples supporting the introduced theory are also given.
