content_image/309662.jpg content_image/309663.jpg content_image/309664.jpg
function representing the output or firing rate of the cell C$_{hl}$ ; and the r $_{−}$neighborhood of the cell C$_{ij}$ is defined as 

<img src='content_image/309662.jpg'>

Motivated by the deficiency of mathematical methods for the investigation of chaos in neural networks on time scales, in the present study, we will consider the following SICNN, 

<img src='content_image/309663.jpg'>

where T 0 = ⋃ ∞ k = $_{−∞}$[ θ$_{2}$$_{k}$$_{−}$$_{1}$, θ$_{2}$$_{k}$ ] and the sequence { θ$_{k}$ }$_{k}$$_{∈}$$_{Z}$ is strictly increasing such that | θ$_{k}$ | → ∞ as | k | → ∞ . The external input L$_{ij}$ ( t, ζ ) is defined through the equation L$_{ij}$ ( t, ζ ) = ζ ij k for t ∈ [ θ$_{2}$$_{k}$$_{−}$$_{1}$, θ$_{2}$$_{k}$ ] , k ∈ Z , such that the sequence ζ = { ζ$_{k}$ }$_{k}$$_{∈}$$_{Z}$ , ζ$_{k}$ = { ζ ij k } ∈ R $^{mn}$, is generated by the map 

<img src='content_image/309664.jpg'>

where F : Λ → Λ is a continuous function and Λ is a compact subset of R $^{mn}$. We assume that ∑ $_{−∞}$( θ$_{2}$$_{k}$ − θ$_{2}$$_{k}$$_{−}$$_{1}$ ) = ∞ and ∑ $^{∞}$( θ$_{2}$$_{k}$ − θ$_{2}$$_{k}$$_{−}$$_{1}$ ) = ∞ . In this paper, the chaotic dynamics of SICNN (1.2) is investigated. We rigorously prove the existence of Li-Yorke chaos in the network (1.2) provided that the map (1.3) is Li-Yorke chaotic. One of the significant features of the obtained chaos is its con- trollability. We also demonstrate the control of the obtained chaos by means of the Pyragas control technique [48]. 

The dynamics of (1.2) is essentially non-autonomous, and it is difficult to verify the ingredients of chaos for unspecified time scales. That is the reason why we utilize the time scale introduced by Akhmet and Turan [47, 68] as well as the reduction technique to impulsive differential equations [47]. 

Artificial neural networks on time scales of the form T 0 can be useful to model neural processes whose instantaneous rate of change cannot be expressed through a differential equation, i.e., not achievable for differential equation analysis. In other words, one can take into account the intervals [ θ$_{2}$$_{k}$$_{−}$$_{1}$, θ$_{2}$$_{k}$ ] , k ∈ Z , as the ones in which the neural processes are achievable so that the instantaneous rate (differential equation) can be obtained experimentally, and the intervals [ θ$_{2}$$_{k}$, θ$_{2}$$_{k}$$_{+1}$ ] , k ∈ Z , can be considered as the ones in which the neural process cannot be achieved. On the other hand, neural processes on time scales which are unions of disjoint compact intervals can be interpreted as activities that work intermittently , i.e., activities that proceed at certain disjoint time intervals and discontinue in between. This type of behavior can be observed in many biological neural activities. For instance, there exist hearth interneurons and motor neurons in the leech whose activities last for about 6 seconds and then the neurons become silent for about 6 seconds [69]. Besides, in Xenopus tadpoles, fictive swimming 

