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.

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.

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 PDϑControl Strategy for a Fractional-Order Chaotic Financial Model

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-14 ◽  
Author(s):  
Changjin Xu ◽  
Maoxin Liao ◽  
Peiluan Li ◽  
Qimei Xiao ◽  
Shuai Yuan
Keyword(s):  
Hopf Bifurcation ◽  
Fractional Order ◽  
Chaotic Behavior ◽  
Sufficient Condition ◽  
Bifurcation Parameter ◽  
Economic Stability ◽  
Financial Model ◽  
The Stability

In this article, based on the previous works, a new fractional-order financial model is put up. The chaotic behavior of the fractional-order financial model is suppressed by designing an appropriatePDϑcontroller. By choosing the delay as the bifurcation parameter, we establish the sufficient condition to guarantee the stability and the existence of Hopf bifurcation of fractional-order financial model. Also, the influence of the delay and the fractional order on the stability and the existence of Hopf bifurcation of fractional-order financial model is revealed. An example is given to confirm the effectiveness of the analysis results. The main findings of this article play an important role in maintaining economic stability.

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.

A Survey of Fractional-Order Neural Networks

2017 ◽  
Author(s):  
Shuo Zhang ◽  
YangQuan Chen ◽  
Yongguang Yu
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Fractional Order ◽  
Computational Science ◽  
General Introduction ◽  
Analysis Methods ◽  
Recent Trends ◽  
The Stability

In this paper, the literature of fractional-order neural networks is categorized and discussed, which includes a general introduction and overview of fractional-order neural networks. Various application areas of fractional-order neural networks have been found or used, and will be surveyed and summarized such as neuroscience, computational science, control and optimization. Recent trends in dynamics of fractional-order neural networks are presented and discussed. The results, especially the stability analysis of fractional-order neural networks, are reviewed and different analysis methods are compared. Furthermore, the challenges and conclusions of fractional-order neural networks are given.

Robust Stochastic Stability of Discrete-Time Markovian Jump Neural Networks with Leakage Delay

2014 ◽  
Vol 69 (1-2) ◽  
pp. 70-80 ◽  
Author(s):  
Mathiyalagan Kalidass ◽  
Hongye Su ◽  
Sakthivel Rathinasamy
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Stochastic Stability ◽  
Leakage Delay ◽  
Linear Matrix ◽  
Stability Criteria ◽  
Markovian Jumping ◽  
Weighting Matrix ◽  
The Stability ◽  
Delay Dependent

This paper presents a robust analysis approach to stochastic stability of the uncertain Markovian jumping discrete-time neural networks (MJDNNs) with time delay in the leakage term. By choosing an appropriate Lyapunov functional and using free weighting matrix technique, a set of delay dependent stability criteria are derived. The stability results are delay dependent, which depend on not only the upper bounds of time delays but also their lower bounds. The obtained stability criteria are established in terms of linear matrix inequalities (LMIs) which can be effectively solved by some standard numerical packages. Finally, some illustrative numerical examples with simulation results are provided to demonstrate applicability of the obtained results. It is shown that even if there is no leakage delay, the obtained results are less restrictive than in some recent works.

Stability and Hopf Bifurcation of Nearest-Neighbor Coupled Neural Networks With Delays

2020 ◽  
Vol 15 (11) ◽  
Author(s):  
Lu Wang ◽  
Min Xiao ◽  
Shuai Zhou ◽  
Yurong Song ◽  
Jinde Cao
Keyword(s):  
Neural Networks ◽  
Hopf Bifurcation ◽  
Nearest Neighbor ◽  
Multiple Delays ◽  
Dimensional System ◽  
Practical Applications ◽  
Coupled Neural Networks ◽  
The Stability ◽  
Related Characteristic ◽  
Theoretical Analyses

Abstract In this paper, a high-dimensional system of nearest-neighbor coupled neural networks with multiple delays is proposed. Nowadays, most present researches about neural networks have studied the connection between adjacent nodes. However, in practical applications, neural networks are extremely complicated. This paper further considers that there are still connection relationships between nonadjacent nodes, which reflect the intrinsic characteristics of neural networks more accurately because of the complexity of its topology. The influences of multiple delays on the local stability and Hopf bifurcation of the system are explored by selecting the sum of delays as bifurcation parameter and discussing the related characteristic equations. It is found that the dynamic behaviors of the system depend on the critical value of bifurcation. In addition, the conditions that ensure the stability of the system and the criteria of Hopf bifurcation are given. Finally, the correctness of the theoretical analyses is verified by numerical simulation.

Finite-time synchronization of delayed fractional-order quaternion-valued memristor-based neural networks

2020 ◽  
pp. 2150032
Author(s):  
Dawei Ding ◽  
Ziruo You ◽  
Yongbing Hu ◽  
Zongli Yang ◽  
Lianghui Ding
Keyword(s):  
Neural Networks ◽  
Fractional Order ◽  
Finite Time ◽  
Time Synchronization ◽  
Linear Part ◽  
State Feedback Control ◽  
Razumikhin Technique ◽  
Quaternion Multiplication ◽  
Control Schemes ◽  
The Stability

This paper mainly concerns with the finite-time synchronization of delayed fractional-order quaternion-valued memristor-based neural networks (FQVMNNs). First, the FQVMNNs are studied by separating the system into four real-valued parts owing to the noncommutativity of quaternion multiplication. Then, two state feedback control schemes, which include linear part and discontinuous part, are designed to guarantee that the synchronization of the studied networks can be achieved in finite time. Meanwhile, in terms of the stability theorem of delayed fractional-order systems, Razumikhin technique and comparison principle, some novel criteria are derived to confirm the synchronization of the studied models. Furthermore, two methods are used to obtain the estimation bounds of settling time. Finally, the feasiblity of the synchronization methods in quaternion domain is validated by the numerical examples.

scholarly journals Complex Behavior Analysis of a Fractional-Order Land Dynamical Model with Holling-II Type Land Reclamation Rate on Time Delay

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Li Wu ◽  
Zhouhong Li ◽  
Yuan Zhang ◽  
Binggeng Xie
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Land Reclamation ◽  
Variable Order ◽  
Transformation Rate ◽  
Complex Behavior ◽  
Bifurcation Parameter ◽  
Type Transformation ◽  
The Stability ◽  
Variable Order Fractional Derivative

In this paper, a fractional-order land model with Holling-II type transformation rate and time delay is investigated. First of all, the variable-order fractional derivative is defined in the Caputo type. Second, by applying time delay as the bifurcation parameter, some criteria to determine the stability and Hopf bifurcation of the model are presented. It turns out that the time delay can drive the model to be oscillatory, even when its steady state is stable. Finally, one numerical example is proposed to justify the validity of theoretical analysis. These results may provide insights to the development of a reasonable strategy to control land-use change.

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