of visual cortical processing, setting the balance between opponent ‘On’ and ‘Off’ responses in different locations of the visual receptive field [44]. On the other hand, shunting neural networks are important for various engineering applications [11],[45]-[53]. For example, in vision, shunting lateral inhibition enhances edges and contrast, mediates directional selectivity, and causes adaptation of the organization of the spatial receptive field and of the contrast sensitivity function [11],[45]-[50]. Moreover, such networks are appropriate to be used in medical diagnosis [53]. Therefore, the investigation of the dynamics of $_{SICNNs,}$which are biologically inspired networks designed upon the shunting inhibition concept [11], is important for the improvement of the techniques used in medical diagnosis, adaptive pattern recognition, image processing etc. [45]-[53] and may shed light on neuronal activities concerning shunting inhibition [42]-[44]. Exponential stability of neural networks has been widely studied in the literature (see, for example, [15]-[18],[54]-[60]). According to Liao et al. [54], the exponential stability has importance in neural net- works when the exponentially convergence rate is used to determine the speed of neural computations. The studies [54, 55] were concerned with the exponential stability and estimation of exponential conver- gence rates in neural networks. In the paper [54], Lyapunov-Krasovskii functionals and the linear matrix inequality (LMI) approaches were combined to investigate the problem, whereas the boundedness of the Dini derivative of the neuron input output activations was required in [55]. The exponential stabilization problem of memristive neural networks was considered in [56] by means of the Lyapunov-Krasovskii func- tional and free weighting matrix techniques. Additionally, the Lyapunov-Krasovskii functional method was considered by Wen et al. [61] to analyze the passivity of stochastic impulsive memristor-based piece- wise linear systems, and the free weighting matrix approach was utilized in [57] to derive an LMI based delay dependent exponential stability criterion for neural networks with a time varying delay. On the other hand, exponential stability criteria were derived by Dan et al. [58] for an error system in order to achieve lag synchronization of coupled delayed chaotic neural networks. The concept of lag synchro- nization was taken into account also within the scope of the papers [62] and [63] for memristive neural networks and for a class of switched neural networks with time-varying delays, respectively. Furthermore, the Banach fixed point theorem and the variant of a certain integral inequality with explicit estimate were used to investigate the global exponential stability of pseudo almost periodic solutions of$_{SICNNs}$ with mixed delays in the study [16]. Almost periodic and in particular quasi-periodic motions are important for the theory of neural net- works. According to Pasemann et al. [64], periodic and quasi-periodic solutions have many fundamental importances in biological and artificial systems, as they are associated with central pattern generators, establishing stability properties and bifurcations (leading to the discovery of periodic solutions). Besides, the sinusoidal shape of neural output signals is, in general, associated with appropriate quasi-periodic attractors for discrete-time dynamical systems. In the book [65], the dynamics of the brain activity is 3