Synchronization of Clifford-valued neural networks with leakage, time-varying, and infinite distributed delays on time scales

Călin-Adrian Popa; Călin-Adrian Popa

doi:10.3934/math.2024915

AIMS Mathematics

2024, Volume 9, Issue 7: 18796-18823. doi: 10.3934/math.2024915

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Research article

Synchronization of Clifford-valued neural networks with leakage, time-varying, and infinite distributed delays on time scales

Călin-Adrian Popa ^,

Department of Computers and Information Technology, Politehnica University of Timişoara, Blvd. V. Pârvan, No. 2, 300223 Timişoara, Romania

Received: 08 February 2024 Revised: 22 April 2024 Accepted: 06 May 2024 Published: 04 June 2024
MSC : 93C10, 93C43, 93D23

Neural networks (NNs) with values in multidimensional domains have lately attracted the attention of researchers. Thus, complex-valued neural networks (CVNNs), quaternion-valued neural networks (QVNNs), and their generalization, Clifford-valued neural networks (ClVNNs) have been proposed in the last few years, and different dynamic properties were studied for them. On the other hand, time scale calculus has been proposed in order to jointly study the properties of continuous time and discrete time systems, or any hybrid combination between the two, and was also successfully applied to the domain of NNs. Finally, in real implementations of NNs, time delays occur inevitably. Taking all these facts into account, this paper discusses ClVNNs defined on time scales with leakage, time-varying delays, and infinite distributed delays, a type of delays which have been relatively rarely present in the existing literature. A state feedback control scheme and a generalization of the Halanay inequality for time scales are used in order to obtain sufficient conditions expressed as algebraic inequalities and as linear matrix inequalities (LMIs), using two general Lyapunov-like functions, for the exponential synchronization of the proposed model. Two numerical examples are given in order to illustrate the theoretical results.
- Clifford-valued neural networks (ClVNNs),
- synchronization analysis,
- time scales,
- time delays,
- infinite distributed delays
Citation: Călin-Adrian Popa. Synchronization of Clifford-valued neural networks with leakage, time-varying, and infinite distributed delays on time scales[J]. AIMS Mathematics, 2024, 9(7): 18796-18823. doi: 10.3934/math.2024915

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Abstract

Neural networks (NNs) with values in multidimensional domains have lately attracted the attention of researchers. Thus, complex-valued neural networks (CVNNs), quaternion-valued neural networks (QVNNs), and their generalization, Clifford-valued neural networks (ClVNNs) have been proposed in the last few years, and different dynamic properties were studied for them. On the other hand, time scale calculus has been proposed in order to jointly study the properties of continuous time and discrete time systems, or any hybrid combination between the two, and was also successfully applied to the domain of NNs. Finally, in real implementations of NNs, time delays occur inevitably. Taking all these facts into account, this paper discusses ClVNNs defined on time scales with leakage, time-varying delays, and infinite distributed delays, a type of delays which have been relatively rarely present in the existing literature. A state feedback control scheme and a generalization of the Halanay inequality for time scales are used in order to obtain sufficient conditions expressed as algebraic inequalities and as linear matrix inequalities (LMIs), using two general Lyapunov-like functions, for the exponential synchronization of the proposed model. Two numerical examples are given in order to illustrate the theoretical results.

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