Pub Date : 2018-09-30DOI: 10.4236/ijmnta.2018.73007
Wen-bing Wu
Complex third-order cumulant has different definition forms. Different forms have different coupling properties, and the generated complex cumulants slices contain different coupling information of signals. In experiments, using the different definitions, the same coupling method is applied to both specific fault signals and normal signals. Furthermore, complex third-order cumulant slices spectrum is defined, and it is used to analyse the coupling features of normal signals and fault signals. Experiments indicate that the detection accuracy rate on the same fault is not the same with the different coupling method, thus, it provides an alternative method to diagnose the specific fault.
{"title":"The Application of Cumulants Slices in Fault Diagnosis","authors":"Wen-bing Wu","doi":"10.4236/ijmnta.2018.73007","DOIUrl":"https://doi.org/10.4236/ijmnta.2018.73007","url":null,"abstract":"Complex third-order cumulant has different definition forms. Different forms have different coupling properties, and the generated complex cumulants slices contain different coupling information of signals. In experiments, using the different definitions, the same coupling method is applied to both specific fault signals and normal signals. Furthermore, complex third-order cumulant slices spectrum is defined, and it is used to analyse the coupling features of normal signals and fault signals. Experiments indicate that the detection accuracy rate on the same fault is not the same with the different coupling method, thus, it provides an alternative method to diagnose the specific fault.","PeriodicalId":69680,"journal":{"name":"现代非线性理论与应用(英文)","volume":"07 1","pages":"89-96"},"PeriodicalIF":0.0,"publicationDate":"2018-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44627858","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-06-29DOI: 10.4236/IJMNTA.2018.72006
Wen-bing Wu, Jin-zhi Xiong, Yupeng Wu, Rihua Liu
Complex three-order cumulant has different definition forms. Different forms conclude different information. For studying the effection of frequency in the coupled signals to fault diagnosis, the differential method to the three order cumulants of coupled signals is adopted. By using the differential of complex three order cumulants before and after respectively, then their dimensional spectrum is calculated, and the results are used to fault diagnosis. The experimental results show that, the increase frequency item in three order cumulants after differentiated impacts on the results of fault diagnosis and the degree of effection is relative to the differential times. And the correct rate of fault diagnosis can be raised by changing the differential times of three order cumulants.
{"title":"The Application of Coupled Three Order Cumulants’ Differential Feature in Fault Diagnosis","authors":"Wen-bing Wu, Jin-zhi Xiong, Yupeng Wu, Rihua Liu","doi":"10.4236/IJMNTA.2018.72006","DOIUrl":"https://doi.org/10.4236/IJMNTA.2018.72006","url":null,"abstract":"Complex three-order cumulant has different definition forms. Different forms conclude different information. For studying the effection of frequency in the coupled signals to fault diagnosis, the differential method to the three order cumulants of coupled signals is adopted. By using the differential of complex three order cumulants before and after respectively, then their dimensional spectrum is calculated, and the results are used to fault diagnosis. The experimental results show that, the increase frequency item in three order cumulants after differentiated impacts on the results of fault diagnosis and the degree of effection is relative to the differential times. And the correct rate of fault diagnosis can be raised by changing the differential times of three order cumulants.","PeriodicalId":69680,"journal":{"name":"现代非线性理论与应用(英文)","volume":"07 1","pages":"77-87"},"PeriodicalIF":0.0,"publicationDate":"2018-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43113033","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-06-12DOI: 10.4236/IJMNTA.2018.72004
S. Shariff
For the model of a Closed Phase Locked Loop (CPLL) communication System consists of both the transmission and receiver ends. This model is considered to be in a multi-order intermittent chaotic state. The chaotic signals are then synchronized along side with our system. This chaotic synchronization will be demonstrated and furthermore, a modulation will be formed to examine the system if it will perfectly reconstruct or not. Finally we will demonstrate the synchronization conditions of the system.
{"title":"Multi-Order Intermittent Chaotic Synchronization of Closed Phase Locked Loop","authors":"S. Shariff","doi":"10.4236/IJMNTA.2018.72004","DOIUrl":"https://doi.org/10.4236/IJMNTA.2018.72004","url":null,"abstract":"For the model of a Closed Phase Locked Loop (CPLL) communication System consists of both the transmission and receiver ends. This model is considered to be in a multi-order intermittent chaotic state. The chaotic signals are then synchronized along side with our system. This chaotic synchronization will be demonstrated and furthermore, a modulation will be formed to examine the system if it will perfectly reconstruct or not. Finally we will demonstrate the synchronization conditions of the system.","PeriodicalId":69680,"journal":{"name":"现代非线性理论与应用(英文)","volume":"07 1","pages":"48-55"},"PeriodicalIF":0.0,"publicationDate":"2018-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46058853","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-06-06DOI: 10.4236/IJMNTA.2018.72005
J. Kharbach, W. Chatar, M. Benkhali, A. Rezzouk, M. Ouazzani-Jamil
In this paper, the integrable classical case of the Hydrogen atom subjected to three static external fields is investigated. The structuring and evolution of the real phase space are explored. The bifurcation diagram is found and the bifurcations of solutions are discussed. The periodic solutions and their associated periods for singular common-level sets of the first integrals of motion are explicitly described. Numerical investigations are performed for the integrable case by means of Poincare surfaces of section and comparing them with nearby living nonintegrable solutions, all generic bifurcations that change the structure of the phase space are illustrated; the problem can exhibit regularity-chaos transition over a range of control parameters of system.
{"title":"On the Regularity and Chaos of the Hydrogen Atom Subjected to External Fields","authors":"J. Kharbach, W. Chatar, M. Benkhali, A. Rezzouk, M. Ouazzani-Jamil","doi":"10.4236/IJMNTA.2018.72005","DOIUrl":"https://doi.org/10.4236/IJMNTA.2018.72005","url":null,"abstract":"In this paper, the integrable classical case of the Hydrogen atom subjected to three static external fields is investigated. The structuring and evolution of the real phase space are explored. The bifurcation diagram is found and the bifurcations of solutions are discussed. The periodic solutions and their associated periods for singular common-level sets of the first integrals of motion are explicitly described. Numerical investigations are performed for the integrable case by means of Poincare surfaces of section and comparing them with nearby living nonintegrable solutions, all generic bifurcations that change the structure of the phase space are illustrated; the problem can exhibit regularity-chaos transition over a range of control parameters of system.","PeriodicalId":69680,"journal":{"name":"现代非线性理论与应用(英文)","volume":"07 1","pages":"56-76"},"PeriodicalIF":0.0,"publicationDate":"2018-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43204248","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-06-06DOI: 10.4236/IJMNTA.2018.72003
Guoguang Lin, Lin-Xia Hu
This paper considers the long-time behavior for a system of coupled wave equations of higher-order Kirchhoff type with strong damping terms. Using the Hadamard graph transformation method, we obtain the existence of the inertial manifold while such equations satisfy the spectral interval condition.
{"title":"The Inertial Manifold for a Class of Nonlinear Higher-Order Coupled Kirchhoff Equations with Strong Linear Damping","authors":"Guoguang Lin, Lin-Xia Hu","doi":"10.4236/IJMNTA.2018.72003","DOIUrl":"https://doi.org/10.4236/IJMNTA.2018.72003","url":null,"abstract":"This paper considers the long-time behavior for a system of coupled wave equations of higher-order Kirchhoff type with strong damping terms. Using the Hadamard graph transformation method, we obtain the existence of the inertial manifold while such equations satisfy the spectral interval condition.","PeriodicalId":69680,"journal":{"name":"现代非线性理论与应用(英文)","volume":"07 1","pages":"35-47"},"PeriodicalIF":0.0,"publicationDate":"2018-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49049711","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-03-26DOI: 10.4236/ijmnta.2018.71002
Zirui Su, Yuting Nie, Fei Xie
Climate change is a global focus over the decades. It triggers many environment issues frequently, even serious natural disasters. The potential effects of the climate change are worse than itself. Many of these effects will gradually weaken the structure of society and government. As a result, the broken governments will turn into fragile states which refer to those states that are not able or choose not to provide the basic essentials to its people. We develop the fuzzy mathematics evaluation model to analyze the problem and evaluate the degree of a country’s fragility, and we definite the fragility evaluation levels through the results in the model. In addition, we also apply our model to Yemen and compare the different situations whether considering climate change or not. Then we put our eyes on South Africa, a getting-warmer country in Africa. We construct the second model—Time series forecasting model, to grasp the changing fragility trend in South Africa and make prediction to see time and ways the fragility degree will change. Furthermore, we modify the forecasting model and use a brand new third model which is called grey model, to figure out the importance of Somalia governmental aid along with intervention by predicting that the arrival of drought in Somalia will be slowed down through positive response from the government.
{"title":"Analysis and Evaluation to a State’s Fragility","authors":"Zirui Su, Yuting Nie, Fei Xie","doi":"10.4236/ijmnta.2018.71002","DOIUrl":"https://doi.org/10.4236/ijmnta.2018.71002","url":null,"abstract":"Climate change is a global focus over the decades. It triggers many environment issues frequently, even serious natural disasters. The potential effects of the climate change are worse than itself. Many of these effects will gradually weaken the structure of society and government. As a result, the broken governments will turn into fragile states which refer to those states that are not able or choose not to provide the basic essentials to its people. We develop the fuzzy mathematics evaluation model to analyze the problem and evaluate the degree of a country’s fragility, and we definite the fragility evaluation levels through the results in the model. In addition, we also apply our model to Yemen and compare the different situations whether considering climate change or not. Then we put our eyes on South Africa, a getting-warmer country in Africa. We construct the second model—Time series forecasting model, to grasp the changing fragility trend in South Africa and make prediction to see time and ways the fragility degree will change. Furthermore, we modify the forecasting model and use a brand new third model which is called grey model, to figure out the importance of Somalia governmental aid along with intervention by predicting that the arrival of drought in Somalia will be slowed down through positive response from the government.","PeriodicalId":69680,"journal":{"name":"现代非线性理论与应用(英文)","volume":"07 1","pages":"16-33"},"PeriodicalIF":0.0,"publicationDate":"2018-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46071864","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-03-07DOI: 10.4236/IJMNTA.2018.71001
Xijuan Liu, Yun Liu
This paper discusses a parasitoid-host-parasitoid ecological model and its dynamical behaviors. On the basis of the center manifold theorem and bi-furcation theory, the existence conditions of the flip bifurcation and Neimark-Sacker bifurcation are derived. In the end of the paper, some typical numerical experiments are performed, which illustrate that the theoretical method is effective.
{"title":"Bifurcation and Chaos in a Parasitoid-Host-Parasitoid Model","authors":"Xijuan Liu, Yun Liu","doi":"10.4236/IJMNTA.2018.71001","DOIUrl":"https://doi.org/10.4236/IJMNTA.2018.71001","url":null,"abstract":"This paper discusses a parasitoid-host-parasitoid ecological model and its dynamical behaviors. On the basis of the center manifold theorem and bi-furcation theory, the existence conditions of the flip bifurcation and Neimark-Sacker bifurcation are derived. In the end of the paper, some typical numerical experiments are performed, which illustrate that the theoretical method is effective.","PeriodicalId":69680,"journal":{"name":"现代非线性理论与应用(英文)","volume":"07 1","pages":"1-15"},"PeriodicalIF":0.0,"publicationDate":"2018-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42446699","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2017-11-27DOI: 10.4236/IJMNTA.2017.64012
Chuangliang Qin, J. Du, Guoguang Lin
In this paper, we investigate the existence of random attractor for the random dynamical system generated by the Kirchhoff-type suspension bridge equations with strong damping and white noises. We first prove the existence and uniqueness of solutions to the initial boundary value conditions, and then we study the existence of the global attractors of the equation.
{"title":"Random Attractors for the Kirchhoff-Type Suspension Bridge Equations with Strong Damping and White Noises","authors":"Chuangliang Qin, J. Du, Guoguang Lin","doi":"10.4236/IJMNTA.2017.64012","DOIUrl":"https://doi.org/10.4236/IJMNTA.2017.64012","url":null,"abstract":"In this paper, we investigate the existence of random attractor for the random dynamical system generated by the Kirchhoff-type suspension bridge equations with strong damping and white noises. We first prove the existence and uniqueness of solutions to the initial boundary value conditions, and then we study the existence of the global attractors of the equation.","PeriodicalId":69680,"journal":{"name":"现代非线性理论与应用(英文)","volume":"06 1","pages":"134-147"},"PeriodicalIF":0.0,"publicationDate":"2017-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49559506","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2017-11-27DOI: 10.4236/IJMNTA.2017.64011
Suqi Ma
To understand dynamical characters of neutrophil dynamical behavior, the sensitivity of delay factors which has effects on system dynamic behavior is ubiquitous due to system’s highly nonlinearity. Here we prove that delay supports a subcritical Hopf bifurcation, underlying a feedback mechanism during stem cells proliferation process while changing its coefficient of amplification. The given cell model reproduces a bistable dynamic regime of blood cells and hysteresis. Applying multiple scale method, oscillation motion near Hopf point is discussed. The stability limit of steady state to be abruptly periodic solution is detected.
{"title":"Periodic Oscillation in Neutrophil Models with Time Delays","authors":"Suqi Ma","doi":"10.4236/IJMNTA.2017.64011","DOIUrl":"https://doi.org/10.4236/IJMNTA.2017.64011","url":null,"abstract":"To understand dynamical characters of neutrophil dynamical behavior, the sensitivity of delay factors which has effects on system dynamic behavior is ubiquitous due to system’s highly nonlinearity. Here we prove that delay supports a subcritical Hopf bifurcation, underlying a feedback mechanism during stem cells proliferation process while changing its coefficient of amplification. The given cell model reproduces a bistable dynamic regime of blood cells and hysteresis. Applying multiple scale method, oscillation motion near Hopf point is discussed. The stability limit of steady state to be abruptly periodic solution is detected.","PeriodicalId":69680,"journal":{"name":"现代非线性理论与应用(英文)","volume":"06 1","pages":"119-133"},"PeriodicalIF":0.0,"publicationDate":"2017-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43666939","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2017-07-24DOI: 10.4236/IJMNTA.2017.63008
A. Liberson, S. Hesler
A family of quasi linear mathematical models is presented and calculations made for viscous turbulent wet steam flow with a variety of condensation phenomena. These models can be applied to the analysis of equilibrium condensation, homogeneous (spontaneous) condensation, heterogeneous condensation on extraneous particles, and condensation of charged dispersed phase moving in an electrostatic field. The unified model is represented by coupled systems of gas dynamic equations for viscous turbulent two-phase flow, kinetic and electro-kinetic equations tracing out combined processes of size and charge growth, and electromagnetic field equations described an electric field with an account of self-induced in-part by a moving electrical cluster. The numerical procedure is time marching, monotone, implicit, of second order accuracy by space and time coordinates, and exhibits high resolution shock capturing ability. Viscous flow field calculations made with this procedure reveal significant influence on condensation by the shear boundary layers and wakes. Distributions of cooling rate, droplet radius and parameters of the bulk flow are predicted. Verification of the codes against known experimental data is presented.
{"title":"A Unified CFD Based Approach to a Variety of Condensation Processes in a Viscous Turbulent Wet Steam Flow","authors":"A. Liberson, S. Hesler","doi":"10.4236/IJMNTA.2017.63008","DOIUrl":"https://doi.org/10.4236/IJMNTA.2017.63008","url":null,"abstract":"A family of quasi linear mathematical models is presented and calculations made for viscous turbulent wet steam flow with a variety of condensation phenomena. These models can be applied to the analysis of equilibrium condensation, homogeneous (spontaneous) condensation, heterogeneous condensation on extraneous particles, and condensation of charged dispersed phase moving in an electrostatic field. The unified model is represented by coupled systems of gas dynamic equations for viscous turbulent two-phase flow, kinetic and electro-kinetic equations tracing out combined processes of size and charge growth, and electromagnetic field equations described an electric field with an account of self-induced in-part by a moving electrical cluster. The numerical procedure is time marching, monotone, implicit, of second order accuracy by space and time coordinates, and exhibits high resolution shock capturing ability. Viscous flow field calculations made with this procedure reveal significant influence on condensation by the shear boundary layers and wakes. Distributions of cooling rate, droplet radius and parameters of the bulk flow are predicted. Verification of the codes against known experimental data is presented.","PeriodicalId":69680,"journal":{"name":"现代非线性理论与应用(英文)","volume":"06 1","pages":"85-97"},"PeriodicalIF":0.0,"publicationDate":"2017-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41480090","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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