scholarly journals Periodic Oscillatory Phenomenon in Fractional-Order Neural Networks Involving Different Types of Delays

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Nengfa Wang ◽  
Changjin Xu ◽  
Zixin Liu
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Hopf Bifurcation ◽  
Fractional Order ◽  
Network Systems ◽  
Different Types ◽  
Variable Substitution ◽  
The Stability ◽  
Distribution Of Roots ◽  
Oscillatory Phenomenon

This research is chiefly concerned with the stability and Hopf bifurcation for newly established fractional-order neural networks involving different types of delays. By means of an appropriate variable substitution, equivalent fractional-order neural network systems involving one delay are built. By discussing the distribution of roots of the characteristic equation of the established fractional-order neural network systems and selecting the delay as bifurcation parameter, a novel delay-independent bifurcation condition is derived. The investigation verifies that the delay is a significant parameter which has an important influence on stability nature and Hopf bifurcation behavior of neural network systems. The computer simulation plots and bifurcation graphs effectively illustrate the reasonableness of the theoretical fruits.

Bifurcations due to different delays of high-order fractional neural networks

2021 ◽  
pp. 2150075
Author(s):  
Chengdai Huang ◽  
Jinde Cao
Keyword(s):  
Neural Networks ◽  
Hopf Bifurcation ◽  
Fractional Order ◽  
Numerical Experiments ◽  
Critical Values ◽  
Communication Delay ◽  
Leakage Delay ◽  
Bifurcation Parameter ◽  
Stability Performance ◽  
The Stability

This paper expounds the bifurcations of two-delayed fractional-order neural networks (FONNs) with multiple neurons. Leakage delay or communication delay is viewed as a bifurcation parameter, stability zones and bifurcation conditions with respect to them are commendably established, respectively. It declares that both leakage delay and communication delay immensely influence the stability and bifurcation of the developed FONNs. The explored FONNs illustrate superior stability performance if selecting a lesser leakage delay or communication delay, and Hopf bifurcation generates once they overstep their critical values. The verification of the feasibility of the developed analytic results is implemented via numerical experiments.

Stability and Synchronization of a Fractional Neutral Higher-Order Neural Network System

2020 ◽  
Vol 21 (5) ◽  
pp. 443-458
Author(s):  
N.-E. Tatar
Keyword(s):  
Neural Network ◽  
Fractional Order ◽  
Neutral Type ◽  
Uniform Boundedness ◽  
Higher Order ◽  
Network System ◽  
Activation Functions ◽  
Network Systems ◽  
Neural Network System ◽  
The Stability

AbstractWe discuss the stability and synchronization of some neural network systems with more than one feature. They are of higher-order, of fractional order and also involving delays of neutral type. Each one of these features presents substantial difficulties to overcome. We prove stability and synchronization of Mittag-Leffler type. This rate is fairly reasonable in case of fractional order. This leads us to prove a neutral fractional version of the well-known Halanay inequality which is interesting by itself. Another feature of the present work is the treatment of unbounded activation functions. The condition of uniform boundedness of the activation functions was commonly used in the literature.

scholarly journals Bifurcation Study on Fractional-Order Cohen–Grossberg Neural Networks Involving Delays

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Bingnan Tang
Keyword(s):  
Neural Networks ◽  
Hopf Bifurcation ◽  
Fractional Order ◽  
Sufficient Criterion ◽  
Software Simulation ◽  
Stability Behavior ◽  
Delayed Neural Networks ◽  
Simulation Results ◽  
Set Up ◽  
The Stability

This work is chiefly concerned with the stability behavior and the appearance of Hopf bifurcation of fractional-order delayed Cohen–Grossberg neural networks. Firstly, we study the stability and the appearance of Hopf bifurcation of the involved neural networks with identical delay ϑ 1 = ϑ 2 = ϑ . Secondly, the sufficient criterion to guarantee the stability and the emergence of Hopf bifurcation for given neural networks with the delay ϑ 2 = 0 is set up. Thirdly, we derive the sufficient condition ensuring the stability and the appearance of Hopf bifurcation for given neural networks with the delay ϑ 1 = 0 . The investigation manifests that the delay plays a momentous role in stabilizing networks and controlling the Hopf bifurcation of the addressed fractional-order delayed neural networks. At last, software simulation results successfully verified the rationality of the analytical results. The theoretical findings of this work can be applied to design, control, and optimize neural networks.

scholarly journals Stability Analysis of a Fractional-Order SEIR-KS Computer Virus-Spreading Model with Two Delays

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Zhufeng Wang ◽  
Xiaoqian Nie ◽  
Maoxin Liao
Keyword(s):  
Hopf Bifurcation ◽  
Fractional Order ◽  
Sufficient Conditions ◽  
Computer Virus ◽  
Bifurcation Theorem ◽  
Different Types ◽  
Two Delays ◽  
Virus Model ◽  
The Stability ◽  
Virus Spreading

In this paper, the stability and Hopf bifurcation of a fractional-order model of the Susceptible-Exposed-Infected-Kill Signals Recovered (SEIR-KS) computer virus with two delays are studied. The sufficient conditions for solving the stability and the occurrence of Hopf bifurcation of the system are established by using Laplace transform, stability theory, and Hopf bifurcation theorem of fractional-order differential systems. The research shows that time delays and fractional order q have an important effect on the stability and the emergence of Hopf bifurcation of the fractional computer virus model. In addition, the validity of the theoretical analysis is verified by selecting appropriate system parameters for numerical simulation and the biological correlation of the equilibrium point is discussed. The results show that the bifurcation point of the model increases with the decrease in the model fractional order q. Under the same fractional order q, the effects of different types of delays on bifurcation points are obviously different.

Squeak and rattle noise classification using radial basis function neural networks

2020 ◽  
Vol 68 (4) ◽  
pp. 283-293
Author(s):  
Oleksandr Pogorilyi ◽  
Mohammad Fard ◽  
John Davy ◽  
Mechanical and Automotive Engineering, School ◽  
Mechanical and Automotive Engineering, School ◽  
...  
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
High Accuracy ◽  
Training Method ◽  
Vehicle Interior ◽  
Trained Classifier ◽  
Different Types ◽  
Noise Classification ◽  
Automatic Tool ◽  
Multi Class Classification

In this article, an artificial neural network is proposed to classify short audio sequences of squeak and rattle (S&R) noises. The aim of the classification is to see how accurately the trained classifier can recognize different types of S&R sounds. Having a high accuracy model that can recognize audible S&R noises could help to build an automatic tool able to identify unpleasant vehicle interior sounds in a matter of seconds from a short audio recording of the sounds. In this article, the training method of the classifier is proposed, and the results show that the trained model can identify various classes of S&R noises: simple (binary clas- sification) and complex ones (multi class classification).

scholarly journals Observer-based adaptive neural network backstepping sliding mode control for switched fractional order uncertain nonlinear systems with unmeasured states

2021 ◽  
pp. 002029402110211
Author(s):  
Tao Chen ◽  
Damin Cao ◽  
Jiaxin Yuan ◽  
Hui Yang
Keyword(s):  
Neural Network ◽  
Nonlinear Systems ◽  
Sliding Mode Control ◽  
Fractional Order ◽  
Sliding Mode ◽  
Tracking Error ◽  
Adaptive Neural Network ◽  
Dynamic Surface ◽  
Mode Control ◽  
The Stability

This paper proposes an observer-based adaptive neural network backstepping sliding mode controller to ensure the stability of switched fractional order strict-feedback nonlinear systems in the presence of arbitrary switchings and unmeasured states. To avoid “explosion of complexity” and obtain fractional derivatives for virtual control functions continuously, the fractional order dynamic surface control (DSC) technology is introduced into the controller. An observer is used for states estimation of the fractional order systems. The sliding mode control technology is introduced to enhance robustness. The unknown nonlinear functions and uncertain disturbances are approximated by the radial basis function neural networks (RBFNNs). The stability of system is ensured by the constructed Lyapunov functions. The fractional adaptive laws are proposed to update uncertain parameters. The proposed controller can ensure convergence of the tracking error and all the states remain bounded in the closed-loop systems. Lastly, the feasibility of the proposed control method is proved by giving two examples.

scholarly journals An Efficient Neural Network-Based Method for Diagnosing Faults of PV Array

2021 ◽  
Vol 13 (11) ◽  
pp. 6194
Author(s):  
Selma Tchoketch_Kebir ◽  
Nawal Cheggaga ◽  
Adrian Ilinca ◽  
Sabri Boulouma
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Modeling Process ◽  
Photovoltaic Arrays ◽  
Mode Of Operation ◽  
Different Types ◽  
The Neural Networks ◽  
Operational Modes ◽  
Types Of Faults ◽  
Electrical Data

This paper presents an efficient neural network-based method for fault diagnosis in photovoltaic arrays. The proposed method was elaborated on three main steps: the data-feeding step, the fault-modeling step, and the decision step. The first step consists of feeding the real meteorological and electrical data to the neural networks, namely solar irradiance, panel temperature, photovoltaic-current, and photovoltaic-voltage. The second step consists of modeling a healthy mode of operation and five additional faulty operational modes; the modeling process is carried out using two networks of artificial neural networks. From this step, six classes are obtained, where each class corresponds to a predefined model, namely, the faultless scenario and five faulty scenarios. The third step involves the diagnosis decision about the system’s state. Based on the results from the above step, two probabilistic neural networks will classify each generated data according to the six classes. The obtained results show that the developed method can effectively detect different types of faults and classify them. Besides, this method still achieves high performances even in the presence of noises. It provides a diagnosis even in the presence of data injected at reduced real-time, which proves its robustness.

scholarly journals Optimal Artificial Neural Network Type Selection Method for Usage in Smart House Systems

Sensors ◽  
2020 ◽  
Vol 21 (1) ◽  
pp. 47
Author(s):  
Vasyl Teslyuk ◽  
Artem Kazarian ◽  
Natalia Kryvinska ◽  
Ivan Tsmots
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Artificial Neural Network ◽  
Artificial Neural Networks ◽  
Input Data ◽  
Optimization Criterion ◽  
Fuzzy Input ◽  
Different Types ◽  
Smart House ◽  
Artificial Neural

In the process of the “smart” house systems work, there is a need to process fuzzy input data. The models based on the artificial neural networks are used to process fuzzy input data from the sensors. However, each artificial neural network has a certain advantage and, with a different accuracy, allows one to process different types of data and generate control signals. To solve this problem, a method of choosing the optimal type of artificial neural network has been proposed. It is based on solving an optimization problem, where the optimization criterion is an error of a certain type of artificial neural network determined to control the corresponding subsystem of a “smart” house. In the process of learning different types of artificial neural networks, the same historical input data are used. The research presents the dependencies between the types of neural networks, the number of inner layers of the artificial neural network, the number of neurons on each inner layer, the error of the settings parameters calculation of the relative expected results.

Turing Instability and Hopf Bifurcation in Cellular Neural Networks

2021 ◽  
Vol 31 (08) ◽  
pp. 2150143
Author(s):  
Zunxian Li ◽  
Chengyi Xia
Keyword(s):  
Neural Networks ◽  
Hopf Bifurcation ◽  
Turing Instability ◽  
Cellular Neural Networks ◽  
Bifurcation Theorem ◽  
Decoupling Method ◽  
Dynamical Behaviors ◽  
The Stability ◽  
Approximate Expressions ◽  
Zero Equilibrium

In this paper, we explore the dynamical behaviors of the 1D two-grid coupled cellular neural networks. Assuming the boundary conditions of zero-flux type, the stability of the zero equilibrium is discussed by analyzing the relevant eigenvalue problem with the aid of the decoupling method, and the conditions for the occurrence of Turing instability and Hopf bifurcation at the zero equilibrium are derived. Furthermore, the approximate expressions of the bifurcating periodic solutions are also obtained by using the Hopf bifurcation theorem. Finally, numerical simulations are provided to demonstrate the theoretical results.

Sign in / Sign up

Export Citation Format

Share Document