In this paper, we use the analysis of relatively dense sets to point out some deficiencies and inaccuracies in the definition of uniformly almost periodic functions which has been proposed in recent works, and we correct it. Some new generalizations of invariance under translation time scales and almost periodic functions are established. Our study will ensure that now we can study almost periodic problems precisely on time scales.

/pdf/relatively-dense-sets-corrected-uniformly-almost-periodic-35kndmu8p2.pdf

Relatively dense sets, corrected uniformly almost periodic functions on time scales, and generalizations

This paper is concerned with a class of neutral-type competitive neural networks with multi-proportional delays, distributed delays and leakage delays. By employing the differential inequality theo...

Global exponential convergence of neutral-type competitive neural networks with multi-proportional delays, distributed delays and time-varying delay in leakage delays

Almost automorphic solution for neutral type high-order Hopfield BAM neural networks with time-varying leakage delays on time scales

This paper is concerned with a class of neutral-type Hopfield neural networks with multi-proportional delays and leakage delays. Using the differential inequality theory, a set of sufficient conditions which guarantee that all solutions of neutral-type Hopfield neural networks with multi-proportional delays and leakage delays converge exponentially to zero vector are derived. Computer simulations are carried out to verify our theoretical findings. The obtained results of this paper are new and complement some previous studies.

Global exponential convergence of neutral-type Hopfield neural networks with multi-proportional delays and leakage delays

Shunting inhibitory cellular neural networks with compartmental periodic unpredictable coefficients and inputs is the focus of this research. A new algorithm is suggested, to enlarge the set of known unpredictable functions by applying diagonalization in arguments of functions of several variables. Sufficient conditions for the existence and uniqueness of exponentially stable unpredictable and Poisson stable outputs are obtained. To attain theoretical results, the included intervals method and the contraction mapping principle are used. Appropriate examples with numerical simulations that support the theoretical results are provided. It is shown how dynamics of the neural network depend on a new numerical characteristic, the degree of periodicity.

/pdf/shunting-inhibitory-cellular-neural-networks-with-2j518mvb.pdf

Shunting Inhibitory Cellular Neural Networks with Compartmental Unpredictable Coefficients and Inputs

In this paper, a class of neutral delay Hopfield neural networks with time-varying delays in the leakage term on time scales is considered. By utilizing the exponential dichotomy of linear dynamic equations on time scales, Banach’s fixed point theorem and the theory of calculus on time scales, some sufficient conditions are obtained for the existence and exponential stability of almost periodic solutions for this class of neural networks. Finally, a numerical example illustrates the feasibility of our results and also shows that the continuous-time neural network and the discrete-time analogue have the same dynamical behaviors. The results of this paper are completely new and complementary to the previously known results even when the time scale .

/pdf/almost-periodic-solutions-for-neutral-delay-hopfield-neural-d767kvfxyl.pdf

Almost periodic solutions for neutral delay Hopfield neural networks with time-varying delays in the leakage term on time scales

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Almost periodic solutions for neutral delay Hopfield neural networks with time-varying delays in the leakage term on time scales