existence of Li-Yorke chaos in a spatiotemporal chaotic system. Moreover, Li-Yorke chaos on several spaces in connection with the cardinality of its scrambled sets was studied within the scope of the paper [33], and generalizations of Li-Yorke chaos to mappings in Banach spaces and complete metric spaces were provided in [34]-[36]. The presence of Li-Yorke chaos in dynamic equations on time scales was first studied in the paper [37]. The extension mechanism of chaos in continuous-time systems can be found in the studies [38]-[46]. To the best of our knowledge, the existence of chaos has never been achieved for neural networks on time scales in the literature before. The main novelty of the present paper is the consideration of chaos for neural networks on time scales. We develop the concept of Li-Yorke chaos for SICNNs on time scales and prove its existence rigorously by making use of the reduction technique to impulsive differential equations, which was introduced by Akhmet and Turan [47]. The results are appropriate to obtain chaotic SICNNs on time scales with arbitrary high number of cells. Another novelty of the present study is the control of chaos on time scales. The Pyragas control method [48]-[51] is utilized to control the chaos in the dynamics of SICNNs on time scales. Our results show that the Pyragas control method is suitable to control chaos not only in continuous-time or discrete-time systems, but also in systems on time scales. It was revealed in the papers [52, 53] that chaotic dynamics is inevitable for brain activities, and it was suggested by Guevara et al. [54] that chaotic behavior may be responsible for dynamical diseases such as schizophrenia, insomnia, epilepsy and dyskinesia. Besides, the presence of chaos in neural networks is useful for separating image segments [55], information processing [56, 57] and synchronization [58]- [61], and it can improve the performance of CNNs on problems that have local minima in energy (cost) functions, since chaotic behavior of CNNs can help the network avoid local minima and reach the global optimum [62]. Moreover, chaos is an important tool in CNNs for the studies of chaotic communication [63]-[66] and combinatorial optimization problems [67]. Let us describe the model of SICNNs in its most original form [3]. 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 hl ij ≥ 0 is the coupling strength of postsynaptic activity of the cell C$_{hl}$ transmitted to the cell C$_{ij}$ ; the activation function f ( x$_{hl}$ ) is a positive continuous 2 x ′ $_{ij}$( t ) = − a$_{ij}$x$_{ij}$ ( t ) − ∑ C$_{hl}$ ∈ N$_{r}$ ( i,j ) C hl ij f ( x$_{hl}$ ( t )) x$_{ij}$ ( t ) + L$_{ij}$ ( t ) , (1.1)