Next Article in Journal
Fabrication of AlCoCrFeNi High-Entropy Alloy Coating on an AISI 304 Substrate via a CoFe2Ni Intermediate Layer
Next Article in Special Issue
Parameter Identification of Fractional-Order Discrete Chaotic Systems
Previous Article in Journal
Stochastic Thermodynamics of Oscillators’ Networks
Previous Article in Special Issue
Identity Vector Extraction by Perceptual Wavelet Packet Entropy and Convolutional Neural Network for Voice Authentication
Article Menu
Issue 1 (January) cover image

Export Article

Open AccessArticle
Entropy 2019, 21(1), 1; https://doi.org/10.3390/e21010001

Dynamics Analysis of a New Fractional-Order Hopfield Neural Network with Delay and Its Generalized Projective Synchronization

1,2,3
,
1,2,3,* and 1,2,3
1
School of Automation, Huazhong University of Science and Technology, 1037 Luoyu Road, Wuhan 430074, China
2
State Key Laboratory of Cryptology, P.O. Box 5159, Beijing 100878, China
3
Key Laboratory of Image Information Processing and Intelligent Control, Ministry of Education, Wuhan 430074, China
*
Author to whom correspondence should be addressed.
Received: 27 November 2018 / Revised: 13 December 2018 / Accepted: 18 December 2018 / Published: 20 December 2018
(This article belongs to the Collection Wavelets, Fractals and Information Theory)
Full-Text   |   PDF [3115 KB, uploaded 20 December 2018]   |  

Abstract

In this paper, a new three-dimensional fractional-order Hopfield-type neural network with delay is proposed. The system has a unique equilibrium point at the origin, which is a saddle point with index two, hence unstable. Intermittent chaos is found in this system. The complex dynamics are analyzed both theoretically and numerically, including intermittent chaos, periodicity, and stability. Those phenomena are confirmed by phase portraits, bifurcation diagrams, and the Largest Lyapunov exponent. Furthermore, a synchronization method based on the state observer is proposed to synchronize a class of time-delayed fractional-order Hopfield-type neural networks. View Full-Text
Keywords: dynamics analysis; fractional-order; Hopfield neural network; generalized projective synchronization dynamics analysis; fractional-order; Hopfield neural network; generalized projective synchronization
Figures

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
SciFeed

Share & Cite This Article

MDPI and ACS Style

Hu, H.-P.; Wang, J.-K.; Xie, F.-L. Dynamics Analysis of a New Fractional-Order Hopfield Neural Network with Delay and Its Generalized Projective Synchronization. Entropy 2019, 21, 1.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top