considered as a system of many coupled oscillators with different incommensurable periods. Signals from the neurons have a phase shift of π/ 2 , and may be useful for various kinds of applications; for instance, controlling the gait of legged robots [66]. Furthermore, an alternative discrete time model of coupled quasi-periodic and chaotic neural network oscillators were considered by Wang [67]. Let us describe the model of SICNNs in its most original form [11]. Consider a two dimensional grid of processing cells arranged into m rows and n columns, and let C$_{ij}$, i = 1 , 2 , . . . , m, j = 1 , 2 , . . . , n, denote the cell at the ( i, j ) position of the lattice. In SICNNs, neighboring cells exert mutual inhibitory interactions of the shunting type. The dynamics of a cell C$_{ij}$ are described by the following nonlinear ordinary differential equation, where x$_{ij}$ is the activity of the cell C$_{ij}$ ; L$_{ij}$ ( t ) is the external input to the cell C$_{ij}$ ; the constant a$_{ij}$ > 0 represents the passive decay rate of the cell activity; C kl ij ≥ 0 is the coupling strength of postsynaptic activity of the cell C$_{kl}$ transmitted to the cell C$_{ij}$ ; the activation function f ( x$_{kl}$ ) is a positive continuous function representing the output or firing rate of the cell C$_{kl}$ ; and the r − neighborhood of the cell C$_{ij}$ is defined as It is worth noting that even if the activation function is supposed to be globally bounded and Lips- chitzian, these properties are not valid for the nonlinear terms in the right hand sides of the differential equations describing the dynamics of SICNNs, and this is one of the reasons why a sophisticated math- ematical analysis is required for SICNNs in general. Another reason is that the connections between neurons in SICNNs act locally only in r − neighborhoods. This causes special ways of evaluations dif- ferent than those customized for earlier developed neural networks in the mathematical analyses of the models. It is reasonable to say that the usage of deviated arguments in neural networks makes the models much closer to applications. For example, in [13] the model was considered with variable delays, In the present study, we introduce and investigate more general neural networks. The model will be described in the next section. dx$_{ij}$ dt = − a$_{ij}$x$_{ij}$ − ∑ C$_{kl}$ ∈ N$_{r}$ ( i,j ) C kl $_{ij}$f ( x$_{kl}$ ( t )) x$_{ij}$ + L$_{ij}$ ( t ) , (1.1) N$_{r}$ ( i, j ) = { C$_{kl}$ : max( | k − i | , | l − j | ) ≤ r, 1 ≤ k ≤ m, 1 ≤ l ≤ n } . dx$_{ij}$ dt = − a$_{ij}$x$_{ij}$ − ∑ C$_{kl}$ ∈ N$_{r}$ ( i,j ) C kl $_{ij}$f ( x$_{kl}$ ( t − τ ( t ))) x$_{ij}$ + L$_{ij}$ ( t ) . (1.2) 4