SICNNs with Li-Yorke chaotic outputs on a time scale

Abstract

In the present study, we investigate the existence of Li-Yorke chaos in the dynamics of shunting inhibitory cellular neural networks (SICNNs) on time scales. It is rigorously proved by taking advantage of external inputs that the outputs of SICNNs exhibit Li-Yorke chaos. The theoretical results are supported by simulations, and the controllability of chaos on the time scale is demonstrated by means of the Pyragas control technique. This is the first time in the literature that the existence as well as the control of chaos are provided for neural networks on time scales.

Unpredictable Solutions of Linear Impulsive Systems

“…Alongside the theory of chaos, impulsive differential equations have also played an essential role from both theoretical and practical points of view over the past few decades [13,[21][22][23][24][25][26][27][28][29][30]. Such differential equations describe dynamics of real world phenomena in which abrupt interruptions of continuous processes are present, and they play a crucial role in various fields such as mechanics, electronics, medicine, neural networks, communication systems, and population dynamics [31][32][33][34][35][36][37][38]. Chaos in the sense of Li-Yorke and the presence of period-doubling route to chaos in impulsive systems were investigated in the studies [39,40] by means of the replication of chaos technique.…”

Modulo periodic Poisson stable solutions of dynamic equations on a time scale

“…Proof. The bounded solution ϕ(s) of system (13), which is defined by (17), can be expressed in the form ϕ(s) = ϕ 1 (s) + ϕ 2 (s), s ∈ R, where…”

“…For details of periodic time scales the reader is referred to [20], and some applications of dynamic equations on such time scales can be found in [10,16,17]. It is worth noting that for each k ∈ Z, the points θ 2k are right-scattered and leftdense, the points θ 2k−1 are left-scattered and right-dense, and σ(θ 2k ) = θ 2k+1 , ρ(θ 2k+1 ) = θ 2k .…”

Existence of positive solutions for fourth‐order impulsive integral boundary value problems on time scales

“…The study unifies the existing results in differential and finite difference equations and provides new powerful tools for exploring connections between the traditionally separated fields. For further information concerning the theory and applications dynamic equations on time scales, we refer the reader to the books [4,5] and the papers [6][7][8][9][10][11][12].…”