Dynamical Effects of Neuron Activation Gradient on Hopfield Neural Network: Numerical Analyses and Hardware Experiments

2019 ◽  
Vol 29 (04) ◽  
pp. 1930010 ◽  
Author(s):  
Bocheng Bao ◽  
Chengjie Chen ◽  
Han Bao ◽  
Xi Zhang ◽  
Quan Xu ◽  
...  
Keyword(s):  
Neural Network ◽  
Control Parameter ◽  
Period Doubling ◽  
Response Speed ◽  
Hopfield Neural Network ◽  
Activation Function ◽  
Numerical Analyses ◽  
Dynamical Behaviors ◽  
Neuron Activation ◽  
Crisis Scenarios

Hyperbolic tangent function, a bounded monotone differentiable function, is usually taken as a neuron activation function, whose activation gradient, i.e. gain scaling parameter, can reflect the response speed in the neuronal electrical activities. However, the previously published literatures have not yet paid attention to the dynamical effects of the neuron activation gradient on Hopfield neural network (HNN). Taking the neuron activation gradient as an adjustable control parameter, dynamical behaviors with the variation of the control parameter are investigated through stability analyses of the equilibrium states, numerical analyses of the mathematical model, and experimental measurements on a hardware level. The results demonstrate that complex dynamical behaviors associated with the neuron activation gradient emerge in the HNN model, including coexisting limit cycle oscillations, coexisting chaotic spiral attractors, chaotic double scrolls, forward and reverse period-doubling cascades, and crisis scenarios, which are effectively confirmed by neuron activation gradient-dependent local attraction basins and parameter-space plots as well. Additionally, the experimentally measured results have nice consistency to numerical simulations.

scholarly journals Analysis and control of the fractional chaotic Hopfield neural network

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Emad E. Mahmoud ◽  
Lone Seth Jahanzaib ◽  
Pushali Trikha ◽  
Omar A. Almaghrabi
Keyword(s):  
Neural Network ◽  
Bifurcation Analysis ◽  
Chaos Control ◽  
Hopfield Neural Network ◽  
Activation Function ◽  
Neuron Activation ◽  
Long Time ◽  
Uniqueness Of The Solution ◽  
And Control ◽  
Adaptive Smc

AbstractThe fractional Hopfield neural network (HNN) model is studied here analyzing its symmetry, uniqueness of the solution, dissipativity, fixed points etc. A Lyapunov and bifurcation analysis of the system is done for specific as well as variable fractional order. Since a very long time ago, HNN has been carefully studied and applied in various fields. Because of the exceptional non-linearity of the neuron activation function, the HNN system is stoutly non-linear. Chaos control using adaptive SMC considering disturbances and uncertainties is done about randomly chosen points by designing suitable controllers. Numerical simulations performed in MATLAB verify the efficacy of the designed controllers.

scholarly journals Nonlinear Dynamics and Chaos in Fractional-Order Hopfield Neural Networks with Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Xia Huang ◽  
Zhen Wang ◽  
Yuxia Li
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Fractional Order ◽  
Hopfield Neural Network ◽  
Hopfield Neural Networks ◽  
Phase Portraits ◽  
Chaotic Attractors ◽  
Chaotic Motions ◽  
Dynamical Behaviors ◽  
Nonlinear Dynamics And Chaos

A fractional-order two-neuron Hopfield neural network with delay is proposed based on the classic well-known Hopfield neural networks, and further, the complex dynamical behaviors of such a network are investigated. A great variety of interesting dynamical phenomena, including single-periodic, multiple-periodic, and chaotic motions, are found to exist. The existence of chaotic attractors is verified by the bifurcation diagram and phase portraits as well.

scholarly journals Memristor Based Binary Convolutional Neural Network Architecture With Configurable Neurons

2021 ◽  
Vol 15 ◽  
Author(s):  
Lixing Huang ◽  
Jietao Diao ◽  
Hongshan Nie ◽  
Wei Wang ◽  
Zhiwei Li ◽  
...  
Keyword(s):  
Neural Network ◽  
Convolutional Neural Network ◽  
High Precision ◽  
Network Architecture ◽  
Large Scale ◽  
Network Performance ◽  
Recognition Accuracy ◽  
Activation Function ◽  
Data Set ◽  
Neuron Activation

The memristor-based convolutional neural network (CNN) gives full play to the advantages of memristive devices, such as low power consumption, high integration density, and strong network recognition capability. Consequently, it is very suitable for building a wearable embedded application system and has broad application prospects in image classification, speech recognition, and other fields. However, limited by the manufacturing process of memristive devices, high-precision weight devices are currently difficult to be applied in large-scale. In the same time, high-precision neuron activation function also further increases the complexity of network hardware implementation. In response to this, this paper proposes a configurable full-binary convolutional neural network (CFB-CNN) architecture, whose inputs, weights, and neurons are all binary values. The neurons are proportionally configured to two modes for different non-ideal situations. The architecture performance is verified based on the MNIST data set, and the influence of device yield and resistance fluctuations under different neuron configurations on network performance is also analyzed. The results show that the recognition accuracy of the 2-layer network is about 98.2%. When the yield rate is about 64% and the hidden neuron mode is configured as −1 and +1, namely ±1 MD, the CFB-CNN architecture achieves about 91.28% recognition accuracy. Whereas the resistance variation is about 26% and the hidden neuron mode configuration is 0 and 1, namely 01 MD, the CFB-CNN architecture gains about 93.43% recognition accuracy. Furthermore, memristors have been demonstrated as one of the most promising devices in neuromorphic computing for its synaptic plasticity. Therefore, the CFB-CNN architecture based on memristor is SNN-compatible, which is verified using the number of pulses to encode pixel values in this paper.

Storage Capacity of Quaternion-Valued Hopfield Neural Networks with Dual Connections

2021 ◽  
pp. 1-15
Author(s):  
Masaki Kobayashi
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Stochastic Analysis ◽  
Storage Capacity ◽  
Hopfield Neural Network ◽  
Activation Function ◽  
Hopfield Neural Networks ◽  
Noise Tolerance ◽  
Complex Valued ◽  
Projection Rule

Abstract A complex-valued Hopfield neural network (CHNN) is a multistate Hopfield model. A quaternion-valued Hopfield neural network (QHNN) with a twin-multistate activation function was proposed to reduce the number of weight parameters of CHNN. Dual connections (DCs) are introduced to the QHNNs to improve the noise tolerance. The DCs take advantage of the noncommutativity of quaternions and consist of two weights between neurons. A QHNN with DCs provides much better noise tolerance than a CHNN. Although a CHNN and a QHNN with DCs have the samenumber of weight parameters, the storage capacity of projection rule for QHNNs with DCs is half of that for CHNNs and equals that of conventional QHNNs. The small storage capacity of QHNNs with DCs is caused by projection rule, not the architecture. In this work, the ebbian rule is introduced and proved by stochastic analysis that the storage capacity of a QHNN with DCs is 0.8 times as many as that of a CHNN.

Complex Dynamics in a Memristive Diode Bridge-Based MLC Circuit: Coexisting Attractors and Double-Transient Chaos

2021 ◽  
Vol 31 (03) ◽  
pp. 2150049
Author(s):  
A. Chithra ◽  
T. Fonzin Fozin ◽  
K. Srinivasan ◽  
E. R. Mache Kengne ◽  
A. Tchagna Kouanou ◽  
...  
Keyword(s):  
Complex Dynamics ◽  
Basin Of Attraction ◽  
Period Doubling ◽  
Transient Chaos ◽  
Multiple Attractors ◽  
Simulation Tools ◽  
Dynamical Behaviors ◽  
Memristive System ◽  
Crisis Scenarios ◽  
Complex Phenomena

This paper uncovers some striking and new complex phenomena in a memristive diode bridge-based Murali–Lakshmanan–Chua (MLC) circuit. These striking dynamical behaviors include the coexistence of multiple attractors and double-transient chaos. Also, period-doubling, chaos, crisis scenarios are observed in the system when varying the amplitude of the external excitation. Numerical simulation tools like phase portrait, cross-section basin of attraction, Lyapunov spectrum, bifurcation diagrams and time series are used to highlight the complex dynamical behaviors in the memristive system. Further, practical realizations of the circuit both in PSpice and real-laboratory measurements match well with the observed numerical simulations.

scholarly journals Piecewise Convex Technique for the Stability Analysis of Delayed Neural Network

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Zixin Liu ◽  
Jian Yu ◽  
Daoyun Xu ◽  
Dingtao Peng
Keyword(s):  
Neural Network ◽  
Time Delays ◽  
Convex Combination ◽  
Uncertain System ◽  
Activation Function ◽  
Positive Matrix ◽  
Neuron Activation ◽  
Delayed Neural Network ◽  
The Stability ◽  
Delay Partitioning

On the basis of the fact that the neuron activation function is sector bounded, this paper transforms the researched original delayed neural network into a linear uncertain system. Combined with delay partitioning technique, by using the convex combination between decomposed time delay and positive matrix, this paper constructs a novel Lyapunov function to derive new less conservative stability criteria. The benefit of the method used in this paper is that it can utilize more information on slope of the activations and time delays. To illustrate the effectiveness of the new established stable criteria, one numerical example and an application example are proposed to compare with some recent results.

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