Lagrange Stability of BAM Quaternion-Valued Inertial Neural Networks via Auxiliary Function-Based Integral Inequalities

Zhao, Rui; Wang, Baoxian; Jian, Jigui

doi:10.1007/s11063-021-10685-6

Cited by 8 publications

(1 citation statement)

References 43 publications

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“…In such practical applications, it is important to consider the dynamics of the designed NNs, particularly their stability. As such, recent studies have investigated various stability methods for BAMNNs and published significant and interesting results [18], [19], [20], [21], [22], [23], [24], [25].…”

Section: Introductionmentioning

confidence: 99%

System Decomposition Method-Based Exponential Stability of Clifford-Valued BAM Delayed Neural Networks

Sriraman,

Balaji,

Veerasivaji

2024

Preprint

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This study explores new theoretical results for the global exponential stability of bidirectional associative memory delayed neural networks in the Clifford domain. By considering time-varying delays, a general class of Clifford-valued bidirectional associative memory neural networks is formulated, which encompasses real-, complex-, and quaternion-valued neural network models as special cases. To analyze the global exponential stability, we first decompose the considered n-dimensional Clifford-valued networks into 2 m n-dimensional real-valued networks, which avoids the inconvenience caused by the non-commutativity of the multiplication of Clifford numbers. Subsequently, we establish new sufficient conditions to guarantee the existence, uniqueness, and global exponential stability of equilibrium points for the considered networks by constructing a new Lyapunov functional and applying homeomorphism theory. Finally, we provide a numerical example accompanied by simulation results to illustrate the validity of the obtained theoretical results. The present results remain valid even when the considered neural networks degenerate into real-, complex-, and quaternion-valued networks.

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Section: Introductionmentioning

confidence: 99%

System Decomposition Method-Based Exponential Stability of Clifford-Valued BAM Delayed Neural Networks

Sriraman,

Balaji,

Veerasivaji

2024

Preprint

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General Decay Synchronization of Fuzzy Inertial Memristive Neural Networks with Discontinuous Activation Function

Chen

Jiang

et al. 2023

Neural Process Lett

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Lagrange Stability of Competitive Neural Networks with Multiple Time-Varying Delays

Tang,

Wang,

Jian

et al. 2024

Neural Process Lett

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In this paper, the Lagrange stability of competitive neural networks (CNNs) with leakage delays and mixed time-varying delays is investigated. By constructing delay-dependent Lyapunov functional, combining inequality analysis technique, the delay-dependent Lagrange stability criterion are obtained in the form of linear matrix inequalities. And the corresponding global exponentially attractive set (GEAS) is obtained. On this basis, by exploring the relationship between the leakage delays and the discrete delay, a better GEAS of the system is obtained from the six different sizes of the two types of delays. Finally, three examples of numerical simulation are given to illustrate the effectiveness of the obtained results.

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Lagrange Stability of BAM Quaternion-Valued Inertial Neural Networks via Auxiliary Function-Based Integral Inequalities

Cited by 8 publications

References 43 publications

System Decomposition Method-Based Exponential Stability of Clifford-Valued BAM Delayed Neural Networks

System Decomposition Method-Based Exponential Stability of Clifford-Valued BAM Delayed Neural Networks

General Decay Synchronization of Fuzzy Inertial Memristive Neural Networks with Discontinuous Activation Function

Lagrange Stability of Competitive Neural Networks with Multiple Time-Varying Delays

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