A Multistable Memristor and Its Application in Fractional-Order Hopfield Neural Network

Wang, Mengjiao; Deng, Bingqing

doi:10.1007/s13538-022-01201-9

Cited by 3 publications

(2 citation statements)

References 35 publications

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“…In addition, it can provide more information capacity and transmission capability, which is of great significance in information processing and communication. Fractional-order chaotic systems have been applied in many scientific fields in recent years, including neural networks [20][21][22][23], economics [24], mechanics [25], and chaotic systems [26][27][28]. The chaotic system has flexibility [29].…”

Section: Introductionmentioning

confidence: 99%

A new 3D fractional-order chaotic system with complex dynamics

Wang,

Dong

2023

Phys. Scr.

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Compared to integer-order chaotic systems, fractional-order chaotic systems have more complex dynamical features due to the introduction of order. The application of fractional-order chaotic systems to chaotic cryptosystems makes the cryptosystems with higher security properties. In this paper, we developed a new 3D fractional-order chaotic system from a 3D integer-order chaotic system, and investigate the dynamical behaviors of this fractional-order system with different parameters and orders. Moreover, self-excited attractors appeared at lower orders through circuit simulations. Furthermore, the synchronization of the new fractional-order chaotic system in the presence of systematic uncertainties and perturbations was achieved using the sliding mode control technique, which sets the stage for the implementation of communication. Finally, offset boosting control was used to investigate the utility of the new chaotic system in engineering applications.

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Section: Introductionmentioning

confidence: 99%

A new 3D fractional-order chaotic system with complex dynamics

Wang,

Dong

2023

Phys. Scr.

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“…The memristor is an effective way to achieve variable connection weights, but the memristor leads to an increase in the dimensionality of the system, which limits the exploration of the dynamics of high-dimensional. The majority of previous outcomes primarily concentrate on HNN consisting of merely 3 or 4 neurons [29][30][31][32][33]. Consequently, the fractional dynamics of complex neural networks with multiple neurons, especially multiple HNNs coupled with memristors, have not been investigated so far.…”

Section: Introductionmentioning

confidence: 99%

Fast Dynamical Analysis of High-dimensional Fractional-Order Memristive-Coupled Hopffeld Neural Networks utilizing a modiffed Non-Classical Methods

Liu,

Chen,

Liu

2023

Preprint

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Solving high-dimensional fractional differential equations has consistently remained one of the most signiffcant challenges within the realm of fractional calculus. Classical numerical methods often grapple with extensive history datasets, resulting in decreased computational efffciency. Existing non-classical methods frequently result in huge dimensional integer-order systems. To address these issues, an improved non-classical method is established in this paper. By introducing an integral interval decomposition strategy, the decay rate of the integrand in the non-classical method is signiffcantly accelerated, achieving a transition from algebraic decay to exponential decay. Consequently, there is a substantial reduction in the dimensionality of the approximate integerorder systems. Simultaneously, the introduction of the interpolation quadrature method further improves the computational accuracy. Theoretical analysis and numerical examples demonstrate that the proposed method offers substantial performance advantages in tackling fractional differential equations. In conclusion, the dynamic behavior of a high-dimensional memristive-coupled Hopffeld neural network was effectively investigated using the proposed method by phase diagrams and bifurcation diagrams. The proposed method demonstrates the capability to accurately identify both chaotic and periodic behavior within the system. Furthermore, it offers a substantial reduction in computation time for high-dimensional systems. This efffciency in capturing complex dynamics while decreasing computational overhead can be highly advantageous in various applications. It holds crucial theoretical implications for the numerical solution of fractional differential equation. Furthermore, it has the potential to foster and stimulate research and practical applications within the realm of fractional order systems.

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