In this paper, the localized properties of lump and interaction solutions to a new extended Jimbo-Miwa (EJM) equation are studied. Based on the Hirota bilinear method and the test function method, the exact solutions of the EJM equation are discussed; the lump soliton solution, lump-kink soliton solution, and periodic lump solution are obtained. Furthermore, the dynamic properties of the obtained solutions are also discussed by graphical simulation. As far as we know, the obtained results have not been reported.
{"title":"Mixed Lump-Stripe Soliton Solutions to a New Extended Jimbo-Miwa Equation","authors":"Ying He","doi":"10.1155/2023/5547696","DOIUrl":"https://doi.org/10.1155/2023/5547696","url":null,"abstract":"In this paper, the localized properties of lump and interaction solutions to a new extended Jimbo-Miwa (EJM) equation are studied. Based on the Hirota bilinear method and the test function method, the exact solutions of the EJM equation are discussed; the lump soliton solution, lump-kink soliton solution, and periodic lump solution are obtained. Furthermore, the dynamic properties of the obtained solutions are also discussed by graphical simulation. As far as we know, the obtained results have not been reported.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48100158","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Xiaolong Shi, Maryam Akhoundi, A. Talebi, M. Mojahedfar
<jats:p>Vague graphs (VGs), which are a family of fuzzy graphs (FGs), are a well-organized and useful tool for capturing and resolving a range of real-world scenarios involving ambiguous data. In graph theory, a dominating set (DS) for a graph <jats:inline-formula> <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"> <msup> <mrow> <mi>G</mi> </mrow> <mrow> <mo>∗</mo> </mrow> </msup> <mo>=</mo> <mfenced open="(" close=")"> <mrow> <mi>X</mi> <mo>,</mo> <mi>E</mi> </mrow> </mfenced> </math> </jats:inline-formula> is a subset <jats:inline-formula> <math xmlns="http://www.w3.org/1998/Math/MathML" id="M2"> <mi mathvariant="fraktur">S</mi> </math> </jats:inline-formula> of the vertices <jats:inline-formula> <math xmlns="http://www.w3.org/1998/Math/MathML" id="M3"> <mi>X</mi> </math> </jats:inline-formula> such that every vertex not in <jats:inline-formula> <math xmlns="http://www.w3.org/1998/Math/MathML" id="M4"> <mi mathvariant="fraktur">S</mi> </math> </jats:inline-formula> is adjacent to at least one member of <jats:inline-formula> <math xmlns="http://www.w3.org/1998/Math/MathML" id="M5"> <mi mathvariant="fraktur">S</mi> </math> </jats:inline-formula>. The concept of DS in FGs has received the attention of many researchers due to its many applications in various fields such as computer science and electronic networks. In this paper, we introduce the notion of <jats:inline-formula> <math xmlns="http://www.w3.org/1998/Math/MathML" id="M6"> <mfenced open="(" close=")"> <mrow> <mfenced open="(" close=")"> <mrow> <msub> <mrow> <mi>ϵ</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub>
{"title":"A Study on Regular Domination in Vague Graphs with Application","authors":"Xiaolong Shi, Maryam Akhoundi, A. Talebi, M. Mojahedfar","doi":"10.1155/2023/7098134","DOIUrl":"https://doi.org/10.1155/2023/7098134","url":null,"abstract":"<jats:p>Vague graphs (VGs), which are a family of fuzzy graphs (FGs), are a well-organized and useful tool for capturing and resolving a range of real-world scenarios involving ambiguous data. In graph theory, a dominating set (DS) for a graph <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\">\u0000 <msup>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mo>∗</mo>\u0000 </mrow>\u0000 </msup>\u0000 <mo>=</mo>\u0000 <mfenced open=\"(\" close=\")\">\u0000 <mrow>\u0000 <mi>X</mi>\u0000 <mo>,</mo>\u0000 <mi>E</mi>\u0000 </mrow>\u0000 </mfenced>\u0000 </math>\u0000 </jats:inline-formula> is a subset <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\">\u0000 <mi mathvariant=\"fraktur\">S</mi>\u0000 </math>\u0000 </jats:inline-formula> of the vertices <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M3\">\u0000 <mi>X</mi>\u0000 </math>\u0000 </jats:inline-formula> such that every vertex not in <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M4\">\u0000 <mi mathvariant=\"fraktur\">S</mi>\u0000 </math>\u0000 </jats:inline-formula> is adjacent to at least one member of <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M5\">\u0000 <mi mathvariant=\"fraktur\">S</mi>\u0000 </math>\u0000 </jats:inline-formula>. The concept of DS in FGs has received the attention of many researchers due to its many applications in various fields such as computer science and electronic networks. In this paper, we introduce the notion of <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M6\">\u0000 <mfenced open=\"(\" close=\")\">\u0000 <mrow>\u0000 <mfenced open=\"(\" close=\")\">\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>ϵ</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msub>\u0000 <mo>,</mo>\u0000 <msub>\u0000 ","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42792036","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Sudipta Gayen, S. Edalatpanah, S. Jha, Ranjan Kumar
This article gives some essential scopes to study the characterizations of the antineutrosophic subgroup and antineutrosophic normal subgroup. Again, several theories and properties have been mentioned which are essential for analyzing their mathematical framework. Moreover, their homomorphic properties have been discussed.
{"title":"On the Characterization of Antineutrosophic Subgroup","authors":"Sudipta Gayen, S. Edalatpanah, S. Jha, Ranjan Kumar","doi":"10.1155/2023/4430103","DOIUrl":"https://doi.org/10.1155/2023/4430103","url":null,"abstract":"This article gives some essential scopes to study the characterizations of the antineutrosophic subgroup and antineutrosophic normal subgroup. Again, several theories and properties have been mentioned which are essential for analyzing their mathematical framework. Moreover, their homomorphic properties have been discussed.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48372304","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we report the effect of classical and quantum superposition of atomic states on quantum correlations. Coupled photon pairs generated in a ladder quantum beat laser using coherent-induced classical field and atomic state coherent superposition are considered. Once the quantum coherence get sufficient time, it can generate quantum correlations that include quantum discord, quantum entanglement, and quantum steering, which quickly increase with time until they get their maximum strength. Their strength can be improved further by increasing the number of superposed atoms per unit time, selecting an appropriate amplitude of the classical fields, and managing the amount of temperatures and phase fluctuations. In particular, two-way quantum steering, which is a guarantee for the existence of quantum discord and quantum entanglement, can be achieved by increasing the rate of atomic injection from 2 kHz to 25 kHz even if the mean temperature of the heat bath is considered. The maximum achievable strength of quantum correlations is enhanced by increasing the rate of atomic injection and choosing an appropriate parameters of the coherent-induced classical field in the open quantum system which is treated by using the density operator approach.
{"title":"Effect of Classical and Quantum Superposition of Atomic States on Quantum Correlations","authors":"Chimdessa Gashu, E. Mosisa, C. Idosa","doi":"10.1155/2023/2729561","DOIUrl":"https://doi.org/10.1155/2023/2729561","url":null,"abstract":"In this paper, we report the effect of classical and quantum superposition of atomic states on quantum correlations. Coupled photon pairs generated in a ladder quantum beat laser using coherent-induced classical field and atomic state coherent superposition are considered. Once the quantum coherence get sufficient time, it can generate quantum correlations that include quantum discord, quantum entanglement, and quantum steering, which quickly increase with time until they get their maximum strength. Their strength can be improved further by increasing the number of superposed atoms per unit time, selecting an appropriate amplitude of the classical fields, and managing the amount of temperatures and phase fluctuations. In particular, two-way quantum steering, which is a guarantee for the existence of quantum discord and quantum entanglement, can be achieved by increasing the rate of atomic injection from 2 kHz to 25 kHz even if the mean temperature of the heat bath is considered. The maximum achievable strength of quantum correlations is enhanced by increasing the rate of atomic injection and choosing an appropriate parameters of the coherent-induced classical field in the open quantum system which is treated by using the density operator approach.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45169943","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The concept of the natural mate and the conjugate curves associated to a smooth curve in Euclidian 3-space were introduced initially by Dashmukh and others. In this paper, we give some extra results that add more properties of the natural mate and the conjugate curves associated with a smooth space curve in E 3 . The position vectors of the natural mate and the conjugate of a given smooth curve are investigated. Also, using the position vector of the natural mate, the necessary and sufficient condition for a smooth given curve to be a Bertrand curve is introduced. Moreover, a new characterization of a general helix is introduced.
{"title":"Position Vectors of the Natural Mate and Conjugate of a Space Curve","authors":"A. Alghanemi, M. Khan","doi":"10.1155/2023/7565988","DOIUrl":"https://doi.org/10.1155/2023/7565988","url":null,"abstract":"The concept of the natural mate and the conjugate curves associated to a smooth curve in Euclidian 3-space were introduced initially by Dashmukh and others. In this paper, we give some extra results that add more properties of the natural mate and the conjugate curves associated with a smooth space curve in \u0000 \u0000 \u0000 \u0000 E\u0000 \u0000 \u0000 3\u0000 \u0000 \u0000 \u0000 . The position vectors of the natural mate and the conjugate of a given smooth curve are investigated. Also, using the position vector of the natural mate, the necessary and sufficient condition for a smooth given curve to be a Bertrand curve is introduced. Moreover, a new characterization of a general helix is introduced.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45564369","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
B. Barnes, Martin Anokye, M. M. Iddrisu, Bismark Gawu, Emmanuel Afrifa
This paper provides a mathematical fractional-order model that accounts for the mindset of patients in the transmission of COVID-19 disease, the continuous inflow of foreigners into the country, immunization of population subjects, and temporary loss of immunity by recovered individuals. The analytic solutions, which are given as series solutions, are derived using the fractional power series method (FPSM) and the residual power series method (RPSM). In comparison, the series solution for the number of susceptible members, using the FPSM, is proportional to the series solution, using the RPSM for the first two terms, with a proportional constant of ψ Γ n α + 1 , where ψ is the natural birth rate of the baby into the susceptible population, Γ is the gamma function, n is the n th term of the series, and α is the fractional order as the initial number of susceptible individuals approaches the population size of Ghana. However, the variation in the two series solutions of the number of members who are susceptible to the COVID-19 disease begins at the third term and continues through the remaining terms. This is brought on by the nonlinear function present in the equation for the susceptible subgroup. The similar finding is made in the series solution of the number of exposed individuals. The series solutions for the number of deviant people, the number of nondeviant people, the number of people quarantined, and the number of people recovered using the FPSM are unquestionably almost identical to the series solutions for same subgroups using the RPSM, with the exception that these series solutions have initial conditions of the subgroup of the population size. It is observed that, in this paper, the series solutions of the nonlinear system of fractional partial differential equations (PDEs) provided by the RPSM are more in line with the field data than the series solutions provided by the FPSM.
{"title":"The Analytic Solutions of the Fractional-Order Model for the Spatial Epidemiology of the COVID-19 Infection","authors":"B. Barnes, Martin Anokye, M. M. Iddrisu, Bismark Gawu, Emmanuel Afrifa","doi":"10.1155/2023/5578900","DOIUrl":"https://doi.org/10.1155/2023/5578900","url":null,"abstract":"This paper provides a mathematical fractional-order model that accounts for the mindset of patients in the transmission of COVID-19 disease, the continuous inflow of foreigners into the country, immunization of population subjects, and temporary loss of immunity by recovered individuals. The analytic solutions, which are given as series solutions, are derived using the fractional power series method (FPSM) and the residual power series method (RPSM). In comparison, the series solution for the number of susceptible members, using the FPSM, is proportional to the series solution, using the RPSM for the first two terms, with a proportional constant of \u0000 \u0000 ψ\u0000 Γ\u0000 \u0000 \u0000 \u0000 \u0000 n\u0000 α\u0000 +\u0000 1\u0000 \u0000 \u0000 \u0000 \u0000 \u0000 , where \u0000 \u0000 ψ\u0000 \u0000 is the natural birth rate of the baby into the susceptible population, \u0000 \u0000 Γ\u0000 \u0000 is the gamma function, \u0000 \u0000 n\u0000 \u0000 is the \u0000 \u0000 n\u0000 \u0000 th term of the series, and \u0000 \u0000 α\u0000 \u0000 is the fractional order as the initial number of susceptible individuals approaches the population size of Ghana. However, the variation in the two series solutions of the number of members who are susceptible to the COVID-19 disease begins at the third term and continues through the remaining terms. This is brought on by the nonlinear function present in the equation for the susceptible subgroup. The similar finding is made in the series solution of the number of exposed individuals. The series solutions for the number of deviant people, the number of nondeviant people, the number of people quarantined, and the number of people recovered using the FPSM are unquestionably almost identical to the series solutions for same subgroups using the RPSM, with the exception that these series solutions have initial conditions of the subgroup of the population size. It is observed that, in this paper, the series solutions of the nonlinear system of fractional partial differential equations (PDEs) provided by the RPSM are more in line with the field data than the series solutions provided by the FPSM.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":"1 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41484662","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Hang Li, Luwei Bai, Jia Yu, Yongmei Mao, Zhenzhen Hui
The informatization construction of the power grid is becoming increasingly popular, business application systems are constantly emerging, and power-related data is rapidly expanding. These discrete power data are scattered in various application systems, and it is not easy to directly provide advanced enterprise applications. The establishment of intelligent power statistical model is an urgent need for constructing power grid informatization. This paper proposes a model of an electric energy metering system based on intelligent sensor data and introduces the existing digital metering system. This model is the integration and promotion of business integration based on the digital metering system. It is the first time to apply new metering equipment, such as measurement and control devices with integrated metering functions, and new metering technologies, such as IEC 61850 electricity meter reading applications. It is hoped that this paper can lay a foundation for further research.
{"title":"Research on Model Construction of Electric Energy Metering System Based on Intelligent Sensor Data","authors":"Hang Li, Luwei Bai, Jia Yu, Yongmei Mao, Zhenzhen Hui","doi":"10.1155/2023/1296165","DOIUrl":"https://doi.org/10.1155/2023/1296165","url":null,"abstract":"The informatization construction of the power grid is becoming increasingly popular, business application systems are constantly emerging, and power-related data is rapidly expanding. These discrete power data are scattered in various application systems, and it is not easy to directly provide advanced enterprise applications. The establishment of intelligent power statistical model is an urgent need for constructing power grid informatization. This paper proposes a model of an electric energy metering system based on intelligent sensor data and introduces the existing digital metering system. This model is the integration and promotion of business integration based on the digital metering system. It is the first time to apply new metering equipment, such as measurement and control devices with integrated metering functions, and new metering technologies, such as IEC 61850 electricity meter reading applications. It is hoped that this paper can lay a foundation for further research.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49400421","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, the effect of a fractional constitutive model on the rheological properties of fluids and its application in numerical simulation are investigated, which is important to characterize the rheological properties of fluids and physical characteristics of materials more accurately. Based on this consideration, numerical simulation and analytical study of unsteady fractional Oldroyd-B viscoelastic flow are carried out. In order to improve the degree of accuracy, the mixed partial derivative including the fractional derivative in the differential equation is converted effectively by integrating by parts instead of by direct discretization. Then, the stability, convergence, and unique solvability of the difference scheme are verified. The validity of the finite difference method is tested by making comparisons with analytical solutions for two kinds of fractional Oldroyd-B viscoelastic flow. Numerical results obtained using the finite difference method are in good agreement with analytical solutions obtained via the variable separation method. Viscoelastic characteristics of the unsteady Poiseuille flow are similar to the second-order fluid or integer-order Oldroyd-B fluid when the parameter is close to 0 or to 1. Oscillation characteristics of fractional viscoelastic oscillatory flow are similar to those of the classical viscoelastic fluid under the same condition. Compared with the previous research, the present work studies the rheological properties of fluids with the finite difference method, and the application of fractional constitutive models in describing the rheological properties of fluids is developed. Meanwhile, more cases reflecting the fractional-order characteristics are given. The present method can accurately capture the flow characteristics of unsteady fractional Oldroyd-B viscoelastic fluid and is applicable for the generalized fractional fluid.
{"title":"A Finite Difference Method for Solving Unsteady Fractional Oldroyd-B Viscoelastic Flow Based on Caputo Derivative","authors":"Fang Wang, Yu Wang","doi":"10.1155/2023/8963904","DOIUrl":"https://doi.org/10.1155/2023/8963904","url":null,"abstract":"In this paper, the effect of a fractional constitutive model on the rheological properties of fluids and its application in numerical simulation are investigated, which is important to characterize the rheological properties of fluids and physical characteristics of materials more accurately. Based on this consideration, numerical simulation and analytical study of unsteady fractional Oldroyd-B viscoelastic flow are carried out. In order to improve the degree of accuracy, the mixed partial derivative including the fractional derivative in the differential equation is converted effectively by integrating by parts instead of by direct discretization. Then, the stability, convergence, and unique solvability of the difference scheme are verified. The validity of the finite difference method is tested by making comparisons with analytical solutions for two kinds of fractional Oldroyd-B viscoelastic flow. Numerical results obtained using the finite difference method are in good agreement with analytical solutions obtained via the variable separation method. Viscoelastic characteristics of the unsteady Poiseuille flow are similar to the second-order fluid or integer-order Oldroyd-B fluid when the parameter is close to 0 or to 1. Oscillation characteristics of fractional viscoelastic oscillatory flow are similar to those of the classical viscoelastic fluid under the same condition. Compared with the previous research, the present work studies the rheological properties of fluids with the finite difference method, and the application of fractional constitutive models in describing the rheological properties of fluids is developed. Meanwhile, more cases reflecting the fractional-order characteristics are given. The present method can accurately capture the flow characteristics of unsteady fractional Oldroyd-B viscoelastic fluid and is applicable for the generalized fractional fluid.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41711474","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper studies the stability criterion of integral time-varying recurrent neural networks (RNNs) with zero lower bound and finite-time synchronization based on improved sliding mode control (SMC). Firstly, a sufficient criterion for universal asymptotic stability of RNNs with integral time-varying delays is obtained by estimating a tight upper bound of augmented Lyapunov-Krasovskii functional (LKF) derivative with inequality scaling technique and mutually convex combined inequality. Secondly, in order to eliminate the time that error system state trajectory slides along sliding mode flow pattern until convergence at the origin, based on drive response and SMC theory, a suitable sliding mode controller is designed by considering that sliding mode flow pattern is equal to synchronization error. Finally, maximum allowable upper bound of delay under different delay derivatives are obtained by considering trajectory change of input function under different initial value. Synchronization trajectory of drive and response systems with mismatched parameters and activation functions under the influence of controller are studied, and synchronization time which is required for error system to reach stability is obtained. Simulation results show that the introduction of integral delay can be more comprehensive from both difference and area, so that drive system state is eventually steady at equilibrium point and synchronized with response system. Stability criterion of this paper not only has less conservative and computation complexity but also has shorter synchronization control time.
{"title":"Stability and Finite-Time Synchronization Analysis for Recurrent Neural Networks with Improved Integral-Type Time-Varying Delays","authors":"Meng Li, Gulijiamali Maimaitiaili","doi":"10.1155/2023/5577859","DOIUrl":"https://doi.org/10.1155/2023/5577859","url":null,"abstract":"This paper studies the stability criterion of integral time-varying recurrent neural networks (RNNs) with zero lower bound and finite-time synchronization based on improved sliding mode control (SMC). Firstly, a sufficient criterion for universal asymptotic stability of RNNs with integral time-varying delays is obtained by estimating a tight upper bound of augmented Lyapunov-Krasovskii functional (LKF) derivative with inequality scaling technique and mutually convex combined inequality. Secondly, in order to eliminate the time that error system state trajectory slides along sliding mode flow pattern until convergence at the origin, based on drive response and SMC theory, a suitable sliding mode controller is designed by considering that sliding mode flow pattern is equal to synchronization error. Finally, maximum allowable upper bound of delay under different delay derivatives are obtained by considering trajectory change of input function under different initial value. Synchronization trajectory of drive and response systems with mismatched parameters and activation functions under the influence of controller are studied, and synchronization time which is required for error system to reach stability is obtained. Simulation results show that the introduction of integral delay can be more comprehensive from both difference and area, so that drive system state is eventually steady at equilibrium point and synchronized with response system. Stability criterion of this paper not only has less conservative and computation complexity but also has shorter synchronization control time.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47128866","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Advances in Information Entropy","authors":"Bin Wang, N. Xiong, F. Xin","doi":"10.1155/2023/9834568","DOIUrl":"https://doi.org/10.1155/2023/9834568","url":null,"abstract":"<jats:p />","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42980412","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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