Changjin Xu

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

This study explores the mechanical aspects of the El-Nino system by transforming it into a Kolmogorov type system, characterized by four types of torques known as internal, inertial, dissipation, and external. Five scenarios by varying these torques to identify the factors that lead to chaos and their physical significance are also investigated. Th...

Delayed dynamical models demonstrate significant application value in depicting interactions and internal dynamics among different biological populations. Therefore, they have garnered significant interest from numerous scholars in both biology and mathematics. Based on previous studies, this article construct a novel delayed predator-prey model. B...

In this paper, the impacts of multiple time delays on bifurcation of a class of fractional nearest-neighbor coupled neural networks are considered. Firstly, the sum of time delays is selected as a parameter, and the fractional nearest-neighbor coupled neural network model is linearized to obtain the corresponding characteristic equation. Then, util...

All the time delayed dynamical system plays a vital role in describing the dynamical phenomenon of neural networks. In the current article, we study a class of 5D delayed bidirectional associative memory (BAM) neural networks that conform to objective reality. First of all, we prove that the solution of the delayed 5D BAM neural networks exists and...

In this current paper, we developed a new predator-prey model accompanying delay based on the earlier works. By applying inequality strategies, fixed point theorem, and a suitable function, we got new necessary conditions for the existence, uniqueness, nonnegativeness, and boundedness of the solution to the developed delayed predator-prey model. Th...

TOP 2% Scientists 2020-2024

Government initiatives, price cuts, and innovations in technology have caused a shift in the world's raw material consumption towards renewable materials. The polymer industry has shown particular interest in studies on more environmentally friendly epoxidation processes that use vegetable oils. Epoxidized vegetable oils are renewable, affordable,...

This article examines adaptive fixed-time difference synchronization for various classes of chaotic dynamical systems. The adaptive fixed-time control technique has been used in this article to investigate the difference synchronization for the Sprott chaotic system, both with and without delay. The fixed settling time (T) has been estimated succes...

Prey and predator are the important factor of the ecosystem. Generally, it is considered that prey-predator models depends on time and it is only required nonlinear system of equations for its dynamical study. But it is observed that such species can move from one to place to another and in such a way there is a need of nonlinear equations which al...

In this work, we investigated the finite-time passivity problem of neutral-type complex-valued neural networks with time-varying delays. On the basis of the Lyapunov functional, Wirtinger-type inequality technique, and linear matrix inequalities (LMIs) approach, new sufficient conditions were derived to ensure the finite-time boundedness (FTB) and...

In this study, the stochastic Chen–Lee–Liu equation is considered numerically and analytically which is forced by the multiplicative noise in the Itô sense. The Chen–Lee–Liu equation is a special type of Schrödinger’s equation which has applications in optical fibers and photonic crystal fibers. The stochastic Crank–Nicolson scheme is formed to obt...

In this current study, novel fractional neural networks owning delay are formulated. Using Lipschitz condition, we demonstrate that the solution of the formulated fractional delayed neural networks exists and is unique. Applying a reasonable function, we handle the boundedness issue of solution to the formulated fractional delayed neural networks....

In this article, we propose a new fractional-order delay-coupled FitzHugh-Nagumo neu-ral model. Taking advantage of delay as a bifurcation parameter, we explore the stability and bifurcation of the formulated fractional-order delay-coupled FitzHugh-Nagumo neural model. A delay-independent stability and bifurcation conditions for the fractional-orde...

Delayed dynamical system plays a vital role in describing the dynamical phenomenon of neural networks. In this article, we proposed a class of new BAM neural networks involving time delay. The traits of solution and bifurcation behavior of the established BAM neural networks involving time delay were probed into. First, the existence and uniqueness...

This work chiefly explores fractional-order octonion-valued neural networks involving delays. We decompose the considered fractional-order delayed octonion-valued neural networks into equivalent real-valued systems via Cayley-Dickson construction. By virtue of Lipschitz condition, we prove that the solution of the considered fractional-order delaye...

Fractional-order differential equations have been proved to have great practical application value in characterizing the dynamical peculiarity in biology. In this article, relying on earlier work, we formulate a new fractional oxygen–plankton model with delay. First of all, the features of the solutions of the fractional delayed oxygen–plankton mod...

The Sasa-Satsuma (SS) equation is studied in this research study using ideas from planar dynamical theory and the beta differential operator. The SS equation is converted into two ordinary differential equations by applying the Galilean transformation. The work is since concentrated on examining the system’s bifurcation points and equilibrium point...

This paper is devoted to the Riemann solutions to the Chaplygin gas dynamics with a single-point heating source. To deal with Dirac measure source term, we transform this model into a system of conservation laws and then present a definition of solution to this system of conservation laws. Based on this definition, we establish, respectively, the c...

The social life, economic issues, and health issues resulting from various diseases will be impacted by the use of the epidemiological model to address the negative effects of drinking in society. The paper aims to investigate a nonlinear drinking epidemic fractional SHTR model in the sense of a Constant Proportional Caputo (CPC) operator. For the...

In this work, we propose fractional-order deterministic mathematical models for human brain information dynamics, including the major effect on sensory memory. The two models are top-down and bottom-up processing. Mathematical models are analysed for different cases for long and short-term memory effects with the effect of experience and prior know...

With the frequent occurrence of financial risks, financial innovation supervision has become an important research issue, and excellent regulatory strategies are of great significance to maintain the stability and sustainable development of financial markets. Thus, this paper intends to analyze the financial regulation strategies through evolutiona...

In an emergency, fear can spread among crowds through one-on-one encounters, with negative societal consequences. The purpose of this research is to create a novel theoretical model of fear (panic) spread in the context of epidemiology during an emergency using the fractal fractional operator. For quantitative analysis, the system’s boundedness and...

Both propagation and collision behavior of \(\delta '\) waves in a model of three partial differential equations are investigated. These are Cauchy problems for this model with initial values involving the first-order derivative of Dirac measure. Based on an \(\alpha \)-solution concept defined in the framework of multiplication of distributions, w...

In the literature \cite{saeed}, the COVID-19 model has been constructed using deterministic approach. The present manuscript examines a stochastic model designed to capture the interplay between COVID-19 and varying infection rates on disease dynamics. We present the necessary criteria for a global solution to the considered model to exist and be u...

This research investigates the presence of unique solutions and quasi-uniform stability for a class of fractional-order uncertain BAM neural networks utilizing the Banach fixed point concept, the contraction mapping principle, and analysis techniques. In order to guarantee the equilibrium point of fractional-order BAM neural networks with undetermi...

The demand for glycerol, a by-product of biodiesel manufacturing , is anticipated to surpass supply, necessitating efficient conversion techniques for sustainability. The importance of effective conversion techniques is illustrated by the development of a system of fractional order differential equations using a literature reaction model. This stud...

Delayed differential equation plays a vital role in revealing the dynamics of chemical reaction law. In this work, we propose a novel fractional-order Lengyel-Epstein model owing time delay. By regarding the delay as parameter and investigating the distribution of roots of the associated characteristic equation of the formulated fractional-order de...

Fish farming, a potential activity for the production of protein with high nutritional value, has emerged as a substantial source of income in the modern world. The degradation of natural materials uses oxygen to reduce them below the life-support stage. A huge area with an excessive amount of water swamp for oxygen exchange makes for the ideal eco...

Recently, delayed dynamical model has witnessed a great interest from many scholars in biological and mathematical areas due to its potential application in describing the interaction of different biological populations. In this article, relying the previous studies, we set up two new predator-prey systems incorporating delay. By virtue of fixed po...

All the time, differential dynamical models with delay has witness a tremendous application value in characterizing the internal law among diverse biological populations in biology. In the current article, on the basis of the previous publications, we formulate a new Lotka–Volterra commensal symbiosis system accompanying delay. Utilizing fixed poin...

Mathematical model plays a significant role in describing the mutual interaction of various chemical compositions in chemistry. In this present work, we formulate a new plankton–oxygen dynamical model owning delay. By virtue of fixed point theorem, inequality techniques and construction of function, we set up the conditions on existence and uniquen...

The Ebola virus continues to be the world’s biggest cause of mortality, especially in developing countries, despite the availability of safe and effective immunization. In this paper, we construct a fractional-order Ebola virus model to check the dynamical transmission of the disease as it is impacted by immunization, learning, prompt identificatio...

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...

In this work, we set up a new discrete predator–prey competitive model with time-varying delays and feedback controls. By virtue of the difference inequality knowledge, a sufficient condition which guarantees the permanence of the established discrete predator–prey competitive model with time-varying delays and feedback controls is derived. Under s...

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...

This work is devoted to establish a numerical scheme for system of fractional-order differential equations (FODEs) with order [Formula: see text]. The scheme is established by using Bernstein polynomials (BPs). Based on the said materials, some operational matrices are formed. With the help of obtained operational matrices, the considered system is...

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 bacteri