Changjin Xu

Guizhou University of Finance and Economics · Guizhou Key Laboratory of Economics System Simulation

In this research, a kind of BAM neural networks containing three nonidentical time delays are explored. Exploiting fixed point knowledge, we examine that the solution to the concerned BAM neural network models exists and is unique. Exploiting a apposite function, we check that the solution to the concerned BAM neural network models is bounded. In l...

Establishing financial models or economic models to describe economic phenomena in real life has become a heated discussion in society at present. From a mathematical point of view, the exploration on dynamics of financial models or economic models is a valuable work. In this study, we build a new delayed finance model and explore the dynamical beh...

Citation: Zhang, Y.; Li, P.; Xu, C.; Peng, X.; Qiao, R. Investigating the Effects of a Fractional Operator on the Evolution of the ENSO Model: Bifurcations, Stability and Numerical Analysis. Fractal Fract. 2023, 7, 602. https://doi.org/10.3390/ fractalfract7080602 Academic Editor: Viorel-Puiu Paun Abstract: Recent years have seen an increase in sci...

MiR‐17‐92 has a vital effect on the adjustment of the Myc/E2F protein in chemistry. In this work, we propose a novel fractional‐order delayed Myc/E2F/miR‐17‐92 network model that revels the relation between miR‐17‐92, E2F, and Myc. Taking advantage of Laplace transform, we obtain the characteristic equation of the established fractional‐order delay...

Fractional-order differential models plays a pivotal role in depicting the relationship among concentration changes of various chemical substances in chemistry. In this current study, we will explore the dynamics of a delayed chemostat model. First of all, we prove that the solution of the delayed chemostat model exists and is unique by virtue of f...

In this paper, the stability and Hopf bifurcation of a six-neuron fractional BAM neural network model with multiple delays are considered. By transforming the multiple-delays model into a fractional-order neural network model with a delay through the variable substitution, we prove the conditions for the existence of Hopf bifurcation at the equilib...

The trait of solution, bifurcation mechanism, and stability of delayed BAM neural network models have attracted great attention from many scholars. But the exploration about the stability aspect and bifurcation mechanism of fractional delayed BAM neural network models is relatively few. This work will focus on the stability aspect and bifurcation m...

Applying delayed dynamical models to characterize the dynamics of neural networks has attracted great interest from scientific community. In this current manuscript, a kind of new tri‐neuron bidirectional associative memory (BAM) neural networks including delay are formulated. The properties of solution and Hopf bifurcation issue of the established...

In order to maximize benefits, oligopolistic competition often occurs in contemporary society. Establishing the mathematical models to reveal the law of market competition has become a vital topic. In the current study, on the basis of the earlier publications, we propose a new fractional-order Bertrand duopoly game model incorporating both noniden...

It is crucial for us to build genetic regulatory models to reveal the relationship between genes and protein efficaciously. In this work, a novel fractional delayed genetic regulatory model is built. For one thing, we explore the peculiarity of the solution of the fractional delayed genetic regulatory model. Some sufficient conditions on the existe...

This paper presents a stochastic model for COVID-19 that takes into account factors such as incubation times, vaccine effectiveness, and quarantine periods in the spread of the virus in symptomatically contagious populations. The paper outlines the conditions necessary for the existence and uniqueness of a global solution for the stochastic model....

https://ojs.wiserpub.com/index.php/CM/SI/Nonlinear_Funct_Fract

The interrelationship between predator populations and prey populations is a central problem in biology and mathematics. Setting up appropriate predator–prey models to portray the development law of predator populations and prey populations has aroused widespread interest in many scholars. In this work, we propose a new fractional order predator–pr...

In this paper, we study the stability and Hopf bifurcation of a class of six-neuron fractional BAM neural networks with multiple delays. Firstly, the model is transformed into a fractional neural network model with two nonidentical delays by using variable substitution. Then, by assigning a value to one of the time delays and selecting the remainin...

In this article, a new 4D hyperchaotic system with torus attractors is developed and analyzed with integer and non-integer order operators. Various dynamical features of the new system are investigated and discussed. The equilibrium points with stability, Lyapunov spectra, Poincaré section, bifurcations, phase portraits, attractors projection, and...

In this study, we principally investigate a fractional‐order stage‐structured predator–prey system including distributed time delays and discrete time delays. Taking advantage of transformation of the variable, we obtain an isovalent version of the considered fractional‐order stage‐structured predator–prey system including distributed time delays a...

In this current study, we formulate a kind of new fractional BAM neural network model concerning five neurons and time delays. First, we explore the existence and uniqueness of the solution of the formulated fractional delay BAM neural network models via the Lipschitz condition. Second, we study the boundedness of the solution to the formulated fra...

Building differential dynamical systems to describe the changing relationship among chemical components is a vital aspect in chemistry. In this present manuscript, we put forward a new fractional-order delayed Brusselator chemical reaction model. By virtue of contraction mapping principle, we investigate the existence and uniqueness of the solution...

In this study, we are concerned with the dynamics of a new established fractional-order delayed zooplankton–phytoplankton system. The existence and uniqueness of the solution are proved via Banach fixed point theorem. Non-negativeness of the solution is studied by mathematical inequality technique. The boundedness of the solution is analyzed by vir...

Delayed differential equation is an important tool to describe the interaction of different chemical substance in chemistry. In this present research, we set up a novel chlorine dioxide-iodine-malonic acid chemical reaction model incorporating delays. The peculiarity of solution and Hopf bifurcation of the formulated delayed chlorine dioxide-iodine...

In this paper, a six-neuron incommensurate fractional order BAM neural network model with multi-delays is considered. We demonstrate that the equilibrium point of the system loses its stability and Hopf bifurcation emerges when the delay passes through a critical value. And the relationship between the critical delay of Hopf bifurcation and size of...

This article is basically concerned with the stability and Hopf bifurcation problem of fractional-order three-triangle multi-delayed neural networks. Based on laplace transform, we obtain the characteristic equation of the considered fractional-order three-triangle multi-delayed neural networks. By discussing the distribution of the roots for the c...

In this study, we analyse the behaviour of the coinfection of the HIV-TB model using a piecewise operator in the classical-Caputo sense. For the aforementioned disease model, we present the existence as well as the uniqueness of a solution having a piecewise derivative. We also study the different versions of stability using Ulam–Hyers stability in...

This paper presents a theoretical and complex numerical analysis of the 2-torus chaotic system with a power-law kernel. Various dynamical characteristics of the complex system are investigated covering existence uniqueness, attractor projection, time series analysis and sensitivity towards initial values. 4-torus attractor coexistence is observed w...

There are many fatal diseases which are caused by virus. Different types of viruses cause different infections. One of them is HIV-1 infection which caused by retrovirus. HIV-1 infection is a hazardous disease that can lead to cancer, AIDS, and other serious illnesses. Several mathematical models have been proposed in the field and examined using v...

Special Issue "State-of-the-Art in Fractional-Order Neural Networks: Theory, Design and Applications" https://www.mdpi.com/journal/fractalfract/special_issues/9BF249UUE2

In the present study, we deal with the stability and the onset of Hopf bifurcation of two type delayed BAM neural networks (integer-order case and fractional-order case). By virtue of the characteristic equation of the integer-order delayed BAM neural networks and regarding time delay as critical parameter, a novel delay-independent condition ensur...

This article analyzes the dynamical evolution of a three-dimensional symmetric oscillator with a fractional Caputo operator. The dynamical properties of the considered model such as equilibria and its stability are also presented. The existence results and uniqueness of solutions for the suggested model are analyzed using the tools from fixed point...

In the study, the sudden act of the cancer model was studied utilizing the fractional operator and its applications to discretize the conformable cancer model. A collection of nonlinear fractional differential equations make up the fractional-order model. We also look at the fractional-order model, which examines how chemotherapeutic attention medi...

In this current manuscript, we study a fractional-order modificatory hybrid optical model (FOMHO model). Experiments manifest that under appropriate parameter conditions, the fractional-order modificatory hybrid optical model will generate chaotic behavior. In order to eliminate the chaotic phenomenon of the (FOMHO model), we devise two different c...

Huanglongbing (yellow dragon disease), often known as citrus greening, is one of the world's most destructive citrus illnesses. It is caused by Candidatus Liberibacter asiaticus, a bacterial disease that spreads through the tree canopy, causing the tree to degrade and eventually die. The aim of this paper is to study the dynamics of the Huanglongbi...

In this study, a class of novel fractional‐order bi‐directional associative memory (BAM) neural networks involving double time delays are put up and investigated. First of all, we prove that the solution of the involved neural networks exists and is unique and bounded. Second of all, we investigate the stability behavior and the onset of Hopf bifur...

Setting up differential models to give a description of the object economical phenomenon in the world today is very essential in economics and mathematics. In this current study, we are committed to the study on the anti‐control of Hopf bifurcation for a fractional‐order stable finance model. By virtue of a suitable washout filter controller involv...

The fractional derivative is an advanced category of mathematics for real-life problems. This work focus on the investigation of 2nd wave of the Corona virus in India. We develop a time-fractional order COVID-19 model with effects of the disease which consist of a system of fractional differential equations. The fractional-order COVID-19 model is i...

This study principally deals with the stability property and the emergence of Hopf bifurcation for fractional-order genetic regulatory networks incorporating distributed delays and discrete delays. By two suitable variable substitutions, we obtain two new equivalent fractional-order differential systems involving only discrete delay. Applying the s...

Recently, the insurance industry in China has been greatly developed. The number of domestic insurance companies and foreign investment insurance companies has greatly increased. Competition between different insurance companies is becoming increasingly fierce. Grasping the internal competition law of different insurance companies is a very meaning...

This paper mainly examines the stability and the existence of Hopf bifurcation of fractional-order BAM neural networks with multiple delays. Based on Laplace transform, stability criterion and Hopf bifurcation theory of fractional-order differential equations, a new sufficient criterion to guarantee the stability and the existence of Hopf bifurcati...

Establishing dynamical models to characterize the relation of different chemical compositions is an important topic in chemistry and mathematics. However, a lot of dynamical models are merely concerned with the integer-order dynamical models. The report on fractional-order chemical dynamical systems is quite few. In this current article, based on t...

In this paper, a Kaldor-Kalecki business cycle model with double delays is considered. By using the stability theory and bifurcation theory of functional differential equations, we obtain the local stability and the conditions of Hopf bifurcation of the system at the equilibrium point. We focus on the impact of consumption delay and investment dela...

In order to reveal the change law of bank data and manage bank effectively, building mathematical models is a very effective approach. In this present study, we set up a novel fractional-order bank data model incorporating two unequal time delays. Firstly, we discuss the existence and uniqueness, non-negativeness, boundedness of the solution to the...

A single paragraph of about 200 words maximum. For research articles, abstracts should provide a pertinent overview of the work. We strongly encourage authors to use the following style of structured abstracts, but without headings: (1) Background: place the question addressed in a broad context and highlight the purpose of the study; (2) Methods:...

During the past several decades, many scholars deal with the stability behavior and Hopf bifurcation phenomenon of fractional-order delayed neural networks. However, the literature involving the stability issue and Hopf bifurcation behavior of fractional-order neural networks with multiple time delays is relatively scarce. This article is principal...

The aim of the article is to analyze the dynamics of Rubella disease model with fractal-fractional exponential decay kernel. Different fractal dimensions and fractional-orders are used to investigate various aspects of the model. It is observed that the considered operator is very effective for the proposed model. The existence and uniqueness of th...

During the past decades, many works on Hopf bifurcation of fractional-order neural networks are mainly concerned with real-valued and complex-valued cases. However, few publications involve the quaternion-valued neural networks which is a generalization of real-valued and complex-valued neural networks. In this present study, we explorate the Hopf...

The aim of the article is to analyze the dynamics of Rubella disease model with fractal-fractional exponential decay kernel. Different fractal dimensions and fractional-orders are used to investigate various aspects of the model. It is observed that the considered operator is very effective for the proposed model. The existence and uniqueness of th...

On the basis of the previous publications, we set up a new fractional-order chaotic finance model. Taking advantage of washout filter controller, we are committed to the study on the chaotic control for the considered fractional-order chaotic finance model. Applying the stability criterion and Hopf bifurcation knowledge of fractional order differen...

Setting up mathematical models to describe the interaction of chemical variables has been a hot issue in chemical and mathematical areas. Nevertheless, many mathematical models are only involved with the integer-order differential equation case. The fruits on fractional-order chemical models are very scarce. In this present work, on the basis of th...

In this study, we propose a novel fractional-order Jerk system. Experiments show that, under some suitable parameters, the fractional-order Jerk system displays a chaotic phenomenon. In order to suppress the chaotic behavior of the fractional-order Jerk system, we design two control strategies. Firstly, we design an appropriate time delay feedback...

This study mainly explores fractional-order six-neuron bi-directional associative memory (BAM) neural networks involving multi-delays. Taking advantage of contraction mapping principle, we prove that the solution of the addressed BAM neural networks exists and is unique. Utilizing a acceptable function, we confirm that the solution of the addressed...

This article is mainly devoted to the investigation on the stability and Hopf bifurcation of fractional-order neural networks with mixed delays. Applying a suitable substitution of variable, a novel equivalent fractional-order neural networks concerning single delay is set up. By analyzing the corresponding characteristic equation of the involved f...

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 char...

This work principally considers the stability issue and the emergence of Hopf bifurcation for a class of fractional-order BAM neural network models concerning time delays. Through the detailed analysis on the distribution of the roots of the characteristic equation of the involved fractional-order delayed BAM neural network systems, we set up a new...

This work principally probes into the stability, the existence, and control of Hopf bifurcation of new established fractional‐order delayed bidirectional associative memory (BAM) neural networks with four neurons. Firstly, based on the earlier study, we set up a class of new fractional‐order multiple delayed BAM neural networks with four neurons. S...

This article investigates quaternion-valued fuzzy cellular neural networks with delays. With the help of fixed point theory, exponential dichotomy of linear equations and related inequalities, some new sufficient conditions which guarantee the existence and global exponentially stability of pseudo almost periodic solutions to quaternion-valued fuzz...

The stability and Hopf bifurcation have important effect on the design of neural networks. By revealing the effect of parameters on the stability and Hopf bifurcation of neural networks, we can better apply neural networks to serve humanity. This article is principally concerned with the stability and the emergence of Hopf bifurcation of fractional...

In this manuscript, quaternion-valued delayed cellular neural networks are studied. Applying the continuation theorem of coincidence degree theory, inequality techniques and a Lyapunov function approach, a new sufficient condition that guarantees the existence and exponential stability of anti-periodic solutions for quaternion-valued delayed cellul...

In the past several decades, many papers involving the stability and Hopf bifurcation of delayed neural networks have been published. However, the results on the stability and Hopf bifurcation for fractional order neural networks with delays and fractional order neural networks with leakage delays are very rare. This paper is concerned with the sta...

In this manuscript, a delayed Nicholson-type model with linear harvesting terms is investigated. Applying coincidence degree theory, we establish a sufficient condition which guarantees the existence of positive periodic solutions for the delayed Nicholson-type model. By constructing suitable Lyapunov functions, a new criterion for the uniqueness a...

During the past decades, integer-order complex-valued neural networks have attracted great attention since they have been widely applied in in many fields of engineering technology. However, the investigation on fractional-order complex-valued neural networks, which are more appropriate to characterize the dynamical nature of neural networks, is ra...

In this paper, we propose a novel fractional-order delayed financial crises contagions model. The stability, Hopf bifurcation and its control of the established fractional-order delayed financial crises contagions model are studied. A delay-independent sufficient condition ensuring the stability and the occurrence of Hopf bifurcation for the fracti...

In the present work, new fractional order BAM neural networks with multiple delays are formulated. Firstly, we study the existence and uniqueness of solution of the constructed neural networks by applying Lipschitz condition. Secondly, the boundedness of solution for the involved neural networks is analyzed by constructing an appropriate function....

In this paper, we propose a new fractional-order financial model which is a generalized version of the financial model reported in the previous publications. By applying a suitable time-delayed feedback controller, we have control for the chaotic behavior of the fractional-order financial model. We investigate the stability and the existence of a H...

This article mainly focuses on the stability and the existence of Hopf bifurcation of integer‐order and fractional‐order two‐neuron neural networks with delay. First of all, we obtain the sufficient criterion to ensure the stability and the existence of Hopf bifurcation of integer‐order two‐neuron neural networks with delay. Next, we establish the...

In this paper, a discrete ratio-dependent food-chain system with delay is investigated. By using Gaines and Mawhin’s continuation theorem of coincidence degree theory and the method of Lyapunov function, a set of sufficient conditions for the existence of positive periodic solutions and global asymptotic stability of the model are established. 1....

In the present work, we mainly focus on shunting inhibitory cellular neural networks (SICNNs) involving leakage delays and proportional delays. By applying the inequality technique, a novel sufficient criterion to ascertain the convergence of every solution of SICNNs with leakage delays and proportional delays is derived. Simulation results are del...

In this manuscript, fuzzy delayed cellular neural networks with impulse are studied. Applying time scale calculus knowledge, mathematical inequalities and constructing Lyapunov function, we establish a sufficient criterion that guarantees the existence and exponential stability of anti-periodic solutions for fuzzy delayed cellular neural networks w...

Abstract We study the weighted pseudo almost periodic solutions of a Lasota–Wazewska system. With the aid of fixed point theory and differential inequality strategies, we give a set of new sufficient criteria that guarantee the existence and global exponential stability of weighted pseudo almost periodic solutions to a Lasota–Wazewska system. The o...

This manuscript mainly deals with quaternion‐valued neural networks (QVNNs) with delays and inertial term. Using Wirtinger inequality and coincidence degree theory, a new sufficient criterion to ensure the existence of antiperiodic solution of involved quaternion‐valued neural networks is derived. With the aid of Lyapunov function, we discuss the e...

This manuscript considers quaternion-valued cellular neural networks with delays. Applying pseudo almost automorphic solution theory of delayed differential equations and pertinent inequalities, a new sufficient criterion to guarantee the existence and global exponentially stability of pseudo almost automorphic solutions of quaternion-valued cellul...