scholarly journals New Stability Criterion for Fractional-Order Quaternion-Valued Neural Networks Involving Discrete and Leakage Delays

2021 ◽  
Vol 2021 ◽  
pp. 1-20
Author(s):  
Bingjun Li ◽  
Bingnan Tang
Keyword(s):  
Neural Networks ◽  
Computer Simulation ◽  
Fractional Order ◽  
Stability Criterion ◽  
Uniform Stability ◽  
Sufficient Criterion ◽  
Leakage Delays ◽  
Analysis Strategy ◽  
Set Up ◽  
Mapping Theory

In the current work, we are devoted to the issue of uniform stability of fractional-order quaternion-valued neural networks involving discrete and leakage delays. Making use of the contracting mapping theory, we prove that the equilibrium point of the involved fractional-order quaternion-valued neural networks exists and is unique. Taking advantage of mathematical analysis strategy, a sufficient criterion involving delay to verify the global uniform stability for the considered fractional-order quaternion-valued neural networks is set up. Computer simulation figures are displayed to sustain the rationality of the established conclusions. This study generalizes and supplements the research of Xiu et al. (2020).

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 Global Synchronization of Reaction-Diffusion Fractional-Order Memristive Neural Networks with Time Delay and Unknown Parameters

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-14 ◽  
Author(s):  
Wenjiao Sun ◽  
Guojian Ren ◽  
Yongguang Yu ◽  
Xudong Hai
Keyword(s):  
Neural Networks ◽  
Time Delay ◽  
Fractional Order ◽  
Reaction Diffusion ◽  
Activation Function ◽  
Memristive Neural Networks ◽  
Unknown Parameters ◽  
Global Synchronization ◽  
Adaptive Controllers ◽  
Mapping Theory

This paper investigated the global synchronization of fractional-order memristive neural networks (FMNNs). To deal with the effect of reaction-diffusion and time delay, fractional partial and comparison theorem are introduced. Based on the set value mapping theory and Filippov solution, the activation function is extended to discontinuous case. Adaptive controllers with a compensator are designed owing to the existence of unknown parameters, with the help of Gronwall–Bellman inequality. Numerical simulation examples demonstrate the availability of the theoretical results.

scholarly journals New stability criterion of neural networks with leakage delays and impulses: a piecewise delay method

2015 ◽  
Vol 10 (1) ◽  
pp. 85-98 ◽  
Author(s):  
R. Suresh Kumar ◽  
G. Sugumaran ◽  
R. Raja ◽  
Quanxin Zhu ◽  
U. Karthik Raja
Keyword(s):  
Neural Networks ◽  
Stability Criterion ◽  
Leakage Delays

scholarly journals Uniform Stability Analysis of Fractional-Order BAM Neural Networks with Delays in the Leakage Terms

2014 ◽  
Vol 2014 ◽  
pp. 1-16 ◽  
Author(s):  
Xujun Yang ◽  
Qiankun Song ◽  
Yurong Liu ◽  
Zhenjiang Zhao
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Equilibrium Point ◽  
Fractional Order ◽  
Sufficient Conditions ◽  
Uniform Stability ◽  
Bam Neural Networks ◽  
Analysis Method ◽  
Inequality Technique ◽  
Delay Dependent

A class of fractional-order BAM neural networks with delays in the leakage terms is considered. By using inequality technique and analysis method, several delay-dependent sufficient conditions are established to ensure the uniform stability of such networks. Moreover, the sufficient conditions guaranteeing the existence, uniqueness, and stability of the equilibrium point are also obtained. In addition, three simulation examples are given to demonstrate the effectiveness of the obtained results.

scholarly journals Further Study on Dynamics for a Fractional-Order Competitor-Competitor-Mutualist Lotka–Volterra System

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Bingnan Tang
Keyword(s):  
Hopf Bifurcation ◽  
Fractional Order ◽  
Natural World ◽  
Volterra Model ◽  
Sufficient Criterion ◽  
Volterra System ◽  
Stability Behavior ◽  
Predator Model ◽  
Set Up ◽  
The Stability

On the basis of the previous publications, a new fractional-order prey-predator model is set up. Firstly, we discuss the existence, uniqueness, and nonnegativity for the involved fractional-order prey-predator model. Secondly, by analyzing the characteristic equation of the considered fractional-order Lotka–Volterra model and regarding the delay as bifurcation variable, we set up a new sufficient criterion to guarantee the stability behavior and the appearance of Hopf bifurcation for the addressed fractional-order Lotka–Volterra system. Thirdly, we perform the computer simulations with Matlab software to substantiate the rationalisation of the analysis conclusions. The obtained results play an important role in maintaining the balance of population in natural world.

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