Weyl almost periodic solutions of octonion-valued high-order fuzzy neural networks with delays

Huang, Xiaoli

doi:10.1007/s40314-023-02294-x

Cited by 5 publications

(1 citation statement)

References 52 publications

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“…The dynamics of recurrent neural networks defined on the algebra of octonions was firstly studied in [11,12]. More recently, other papers have appeared that discuss dynamic properties of OVNNs, for example, [13][14][15][16]. We can observe an increasing interest in studying OVNNs in the last two years, which means that the domain of OVNNs is captivating the attention of the research community and that more papers will appear in the very near future.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic and Mittag–Leffler Synchronization of Fractional-Order Octonion-Valued Neural Networks with Neutral-Type and Mixed Delays

Popa

2023

Fractal Fract

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Very recently, a different generalization of real-valued neural networks (RVNNs) to multidimensional domains beside the complex-valued neural networks (CVNNs), quaternion-valued neural networks (QVNNs), and Clifford-valued neural networks (ClVNNs) has appeared, namely octonion-valued neural networks (OVNNs), which are not a subset of ClVNNs. They are defined on the octonion algebra, which is an 8D algebra over the reals, and is also the only other normed division algebra that can be defined over the reals beside the complex and quaternion algebras. On the other hand, fractional-order neural networks (FONNs) have also been very intensively researched in the recent past. Thus, the present work combines FONNs and OVNNs and puts forward a fractional-order octonion-valued neural network (FOOVNN) with neutral-type, time-varying, and distributed delays, a very general model not yet discussed in the literature, to our awareness. Sufficient criteria expressed as linear matrix inequalities (LMIs) and algebraic inequalities are deduced, which ensure the asymptotic and Mittag–Leffler synchronization properties of the proposed model by decomposing the OVNN system of equations into a real-valued one, in order to avoid the non-associativity problem of the octonion algebra. To accomplish synchronization, we use two different state feedback controllers, two different types of Lyapunov-like functionals in conjunction with two Halanay-type lemmas for FONNs, the free-weighting matrix method, a classical lemma, and Young’s inequality. The four theorems presented in the paper are each illustrated by a numerical example.

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Section: Introductionmentioning

confidence: 99%

Asymptotic and Mittag–Leffler Synchronization of Fractional-Order Octonion-Valued Neural Networks with Neutral-Type and Mixed Delays

Popa

2023

Fractal Fract

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Besicovitch Almost Anti-periodic Solution of Octonion-Valued Cohen–Grossberg Neural Networks with Delays on Time Scales

Li,

2024

Neural Process Lett

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In this work, we put forward a concept of Besicovitch almost anti-periodic functions on time scales, which is new even when time scale $$\mathbb {T}=\mathbb {R}$$ T = R or $$\mathbb {Z}$$ Z . Based on this, we use the fixed point theorem and analytical techniques to obtain the existence, uniqueness and global exponential stability of Besicovitch almost anti-periodic solutions for a class of octonion-valued Cohen–Grossberg neural networks with time delays on time scales. Finally, the validity of the results is verified by a numerical example.

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Stability and synchronization of octonion-valued neural networks with leakage and mixed delays on time scales

Popa

2024

Comp. Appl. Math.

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There has been a great deal of interest in the last few years for neural networks (NNs) with values in multidimensional domains. The most popular models are complex-valued neural networks (CVNNs), followed by quaternion-valued neural networks (QVNNs), and, more recently, by Clifford-valued neural networks (ClVNNs). However, also very recently, a different type of NNs were put forward, namely octonion-valued neural networks (OVNNs). OVNNs are defined on the 8D octonion algebra, and they are not a special type of ClVNNs, because Clifford numbers are associative, whereas octonions are not. Moreover, beside the complex and quaternion algebras, the only other normed division algebra over the reals is the algebra of octonions, which makes OVNNs a direct generalization of CVNNs and QVNNs from this point of view, raising interest for applications handling high-dimensional data. On the other hand, systems defined on time scales were proposed as a generalization of both discrete time and continuous time systems, or any type of hybrid combination between the two. Finally, time delays appear as a consequence of implementing NNs in real life circuits. Taking all these into consideration, this paper studies the fundamental properties of exponential stability and exponential synchronization for OVNNs with leakage and mixed delays defined on time scales. In order to avoid the problems raised by the non-associativity of the octonion algebra, the OVNN model is decomposed into a real-valued one. Then, two different Lyapunov-type functionals are defined and the particularities of time scale calculus are used in order to deduce sufficient conditions expressed as scalar and linear matrix inequalities (LMIs) for the exponential stability of the proposed models, based on Halanay-type inequalities suitable for time scale systems. Afterwards, a state feedback controller is used to deduce sufficient criteria given as scalar inequalities and LMIs for the exponential synchronization of the same type of models. The generality of the model, given by the definition on the algebra of octonions, the use of different types of delays, and the definition on time scales represent an important advantage. Also, for less general models, it is possible to particularize the obtained results. With the aim to demonstrate each of the paper’s four theorems, four numerical examples are provided.

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Weyl almost periodic solutions of octonion-valued high-order fuzzy neural networks with delays

Cited by 5 publications

References 52 publications

Asymptotic and Mittag–Leffler Synchronization of Fractional-Order Octonion-Valued Neural Networks with Neutral-Type and Mixed Delays

Asymptotic and Mittag–Leffler Synchronization of Fractional-Order Octonion-Valued Neural Networks with Neutral-Type and Mixed Delays

Besicovitch Almost Anti-periodic Solution of Octonion-Valued Cohen–Grossberg Neural Networks with Delays on Time Scales

Stability and synchronization of octonion-valued neural networks with leakage and mixed delays on time scales

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