In this paper, a Cauchy problem for two-dimensional Lap lace equation in the strip 0 ≤ × ≤ 1 is considered. This is a classical severely ill-posed problem. Connecting Shannon wavelet bases with a spectral integral of the Hermitian operator, we can obtain a regularized solution. Moreover, some sharp stable estimates between the exact solution and it's approximation is also provided.
{"title":"Optimal Wavelet Solutions for Ill-posed Elliptic Equations","authors":"Jinru Wang, Meng Wang","doi":"10.1109/IWCFTA.2012.11","DOIUrl":"https://doi.org/10.1109/IWCFTA.2012.11","url":null,"abstract":"In this paper, a Cauchy problem for two-dimensional Lap lace equation in the strip 0 ≤ × ≤ 1 is considered. This is a classical severely ill-posed problem. Connecting Shannon wavelet bases with a spectral integral of the Hermitian operator, we can obtain a regularized solution. Moreover, some sharp stable estimates between the exact solution and it's approximation is also provided.","PeriodicalId":354870,"journal":{"name":"2012 Fifth International Workshop on Chaos-fractals Theories and Applications","volume":"386 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122849296","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}
The impulsive synchronization of spatiotemporal chaos is investigated. A proof of the existence of a certain kind of impulses for synchronization such that the error dynamics is equi-attractive in the large is established. The method of choosing impulse duration and the magnitude of the impulses is discussed in detail. Moreover, as an application, a secure communication scheme based on the results of this paper is developed. It's concluded that the simulation results verify the proposed scheme's success in the communication application.
{"title":"Impulsive Synchronization of Kuramoto-Sivashinsky System and its Appliction to Secure Communication","authors":"Hongyan Li, Wanli Yang, Suwen Zheng, Yucai Dong","doi":"10.1109/IWCFTA.2012.61","DOIUrl":"https://doi.org/10.1109/IWCFTA.2012.61","url":null,"abstract":"The impulsive synchronization of spatiotemporal chaos is investigated. A proof of the existence of a certain kind of impulses for synchronization such that the error dynamics is equi-attractive in the large is established. The method of choosing impulse duration and the magnitude of the impulses is discussed in detail. Moreover, as an application, a secure communication scheme based on the results of this paper is developed. It's concluded that the simulation results verify the proposed scheme's success in the communication application.","PeriodicalId":354870,"journal":{"name":"2012 Fifth International Workshop on Chaos-fractals Theories and Applications","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123969917","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}
The concepts of chaotic quasi-random variables and chaotic quasi-random process are proposed in this paper. The study focuses on viewing from a new viewpoint to descript chaotic signal generated by Logistic mapping for communication. We find that although chaos has essential difference from random, it also can be seen by a new view to some extent. This paper shows the probability, with theoretical derivation and simulation results. Thereafter, it can provide a new way for us to understand the relationship of chaos and random.
{"title":"A New Viewpoint on Chaotic Signal in Communication: Viewing from Random Variables and Random Process","authors":"Jing Pan, Yan-Bin Zheng, Lei Ning, Q. Ding","doi":"10.1109/IWCFTA.2012.46","DOIUrl":"https://doi.org/10.1109/IWCFTA.2012.46","url":null,"abstract":"The concepts of chaotic quasi-random variables and chaotic quasi-random process are proposed in this paper. The study focuses on viewing from a new viewpoint to descript chaotic signal generated by Logistic mapping for communication. We find that although chaos has essential difference from random, it also can be seen by a new view to some extent. This paper shows the probability, with theoretical derivation and simulation results. Thereafter, it can provide a new way for us to understand the relationship of chaos and random.","PeriodicalId":354870,"journal":{"name":"2012 Fifth International Workshop on Chaos-fractals Theories and Applications","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115445167","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}
Renewable power generation systems are gaining popularity and have developed quickly in recent years. However, due to the intermittent features of the renewable energy sources, conversion systems involving more than one energy sources are usually designed with multiple structures and multiple operating modes. The dynamic behavior is thus quite complex, and the design for stable operation of such systems requires consideration of the stability conditions for all possible structures and operation modes. This paper describes such conversion systems, and uses a standalone photovoltaic-battery hybrid power system as an example for illustrating the possible complex behavior. We reveal smooth and non-smooth bifurcation phenomena in this system. Under certain conditions, when the system switches its operation mode, a non-smooth bifurcation has been observed and verified with full-circuit simulations. Moreover, a detailed analysis based on an averaged model is performed to identify the two types of bifurcation.
{"title":"Smooth and Non-smooth Bifurcations in Multi-structure Multi-operating-mode Systems: Case Study of a Power Conversion System with Two Energy Sources","authors":"Xiaoling Xiong, C. Tse, X. Ruan","doi":"10.1109/IWCFTA.2012.42","DOIUrl":"https://doi.org/10.1109/IWCFTA.2012.42","url":null,"abstract":"Renewable power generation systems are gaining popularity and have developed quickly in recent years. However, due to the intermittent features of the renewable energy sources, conversion systems involving more than one energy sources are usually designed with multiple structures and multiple operating modes. The dynamic behavior is thus quite complex, and the design for stable operation of such systems requires consideration of the stability conditions for all possible structures and operation modes. This paper describes such conversion systems, and uses a standalone photovoltaic-battery hybrid power system as an example for illustrating the possible complex behavior. We reveal smooth and non-smooth bifurcation phenomena in this system. Under certain conditions, when the system switches its operation mode, a non-smooth bifurcation has been observed and verified with full-circuit simulations. Moreover, a detailed analysis based on an averaged model is performed to identify the two types of bifurcation.","PeriodicalId":354870,"journal":{"name":"2012 Fifth International Workshop on Chaos-fractals Theories and Applications","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123850420","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}
As digital chaos is affected by the limited precision of computer, chaotic sequence properties present short periodicity. For the phenomenon of digital chaos, the paper analyzes similar-short periodicity of digital chaos and puts forward a novel generator of digital chaos key sequence. Meanwhile, we detail the DCT (Discrete Cosine Transformation) compression and Wavelet compression method, and then make comparison for their different performances. Finally, this paper selects the better compressed image, and then uses new chaotic sequence to encrypt the compressed image.
{"title":"Similar-short Periodicity Analysis and Application in Image Compression Encryption of Digital Chaos","authors":"Xiaoli Geng, Q. Ding","doi":"10.1109/IWCFTA.2012.44","DOIUrl":"https://doi.org/10.1109/IWCFTA.2012.44","url":null,"abstract":"As digital chaos is affected by the limited precision of computer, chaotic sequence properties present short periodicity. For the phenomenon of digital chaos, the paper analyzes similar-short periodicity of digital chaos and puts forward a novel generator of digital chaos key sequence. Meanwhile, we detail the DCT (Discrete Cosine Transformation) compression and Wavelet compression method, and then make comparison for their different performances. Finally, this paper selects the better compressed image, and then uses new chaotic sequence to encrypt the compressed image.","PeriodicalId":354870,"journal":{"name":"2012 Fifth International Workshop on Chaos-fractals Theories and Applications","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114977190","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}
In this paper, an existence result of positive solutions for some three-point boundary value problems is obtained by using Leray-Schauder nonlinear alternative.
本文利用Leray-Schauder非线性替代方法，得到了一类三点边值问题正解的存在性结果。
{"title":"Positive Solutions for Some Three-point Boundary Value Problems","authors":"Lei Wang","doi":"10.1109/IWCFTA.2012.25","DOIUrl":"https://doi.org/10.1109/IWCFTA.2012.25","url":null,"abstract":"In this paper, an existence result of positive solutions for some three-point boundary value problems is obtained by using Leray-Schauder nonlinear alternative.","PeriodicalId":354870,"journal":{"name":"2012 Fifth International Workshop on Chaos-fractals Theories and Applications","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125071457","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}
Jiahui Liu, Hongli Zhang, Dahua Song, M. Buza, Bo Yang, Cong Guo
In this paper, iteration method of logistic map with low positions is introduced in order to investigate property of logistic map. Basic structure of logistic map is proposed, which consists of common gene positions (CGPs) and individual gene positions (IGPs). CGPs have the same value of corresponding positions which transferred from previous numerical solutions. The ergodicity and long-term unpredictability of logistic map are largely dependent on IGPs. CGPs and IGPs can help us to deeply understand the property of chaos.
{"title":"A New Property of Logistic Map with Scalable Precision","authors":"Jiahui Liu, Hongli Zhang, Dahua Song, M. Buza, Bo Yang, Cong Guo","doi":"10.1109/IWCFTA.2012.24","DOIUrl":"https://doi.org/10.1109/IWCFTA.2012.24","url":null,"abstract":"In this paper, iteration method of logistic map with low positions is introduced in order to investigate property of logistic map. Basic structure of logistic map is proposed, which consists of common gene positions (CGPs) and individual gene positions (IGPs). CGPs have the same value of corresponding positions which transferred from previous numerical solutions. The ergodicity and long-term unpredictability of logistic map are largely dependent on IGPs. CGPs and IGPs can help us to deeply understand the property of chaos.","PeriodicalId":354870,"journal":{"name":"2012 Fifth International Workshop on Chaos-fractals Theories and Applications","volume":"248 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120896787","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}
In this paper a hyper-chaotic cryptosystem is proposed based on two encryption processes: the image substitution permutation cryptography process followed by masking of the ciphered image. In the substitution-permutation cryptography process, the selective encryption using exclusive or operation is performed in the frequency domain, and the image is further encrypted in the spatial domain using the permutation encryption rule and keys generated by the Qi hyper-chaotic system. The ciphered image is changed into a time varying series which is fed into the hyper-chaotic transmitter as a driving signal. The unmasking process is proposed based on a model-free multivariable high order differential feedback controller used to synchronize the driven and the response systems of our scheme. Analysis and result have shown that the model-free controller offers a robust synchronization and the two encrypting processes for image increase the image security.
{"title":"Hyper-Chaotic Cryptosystem Using Model-free Synchronization","authors":"Guoyuan Qi, S. B. Matondo","doi":"10.1109/IWCFTA.2012.48","DOIUrl":"https://doi.org/10.1109/IWCFTA.2012.48","url":null,"abstract":"In this paper a hyper-chaotic cryptosystem is proposed based on two encryption processes: the image substitution permutation cryptography process followed by masking of the ciphered image. In the substitution-permutation cryptography process, the selective encryption using exclusive or operation is performed in the frequency domain, and the image is further encrypted in the spatial domain using the permutation encryption rule and keys generated by the Qi hyper-chaotic system. The ciphered image is changed into a time varying series which is fed into the hyper-chaotic transmitter as a driving signal. The unmasking process is proposed based on a model-free multivariable high order differential feedback controller used to synchronize the driven and the response systems of our scheme. Analysis and result have shown that the model-free controller offers a robust synchronization and the two encrypting processes for image increase the image security.","PeriodicalId":354870,"journal":{"name":"2012 Fifth International Workshop on Chaos-fractals Theories and Applications","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130930389","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}
Fractal Market Hypothesis (FMH) was originated in 1960s and formulated in 1990s. As one of the forward theories in mathematical finance, FMH has offered a new prospect and methodology for the nonlinear dynamical capital market. This paper tentatively analyzes the cross-development between EMH and FMH, as well as the application and tendency of FMH. We firstly clarificate that FMH is not a substitution or alternative but a complement to EMH, and reveal that the intrinsic unity is their essential relationship. Then we emphasize repeatedly that studies of domestic mostly remain at initial stage. There have been too many empirical analyses to demonstrate the fractal structure of market, but relatively too little work of what the microscopic causes are or how to conduct portfolio selection and risk management according to FMH. Our basic discussion is supposed to conclude the logicality between different theories and application prospects of FMH. We hope cautiously that our personal views could inspire some guidance for further research.
{"title":"EMH and FMH: Origin, Evolution and Tendency","authors":"Guangyuan Song, Guang Liu","doi":"10.1109/IWCFTA.2012.71","DOIUrl":"https://doi.org/10.1109/IWCFTA.2012.71","url":null,"abstract":"Fractal Market Hypothesis (FMH) was originated in 1960s and formulated in 1990s. As one of the forward theories in mathematical finance, FMH has offered a new prospect and methodology for the nonlinear dynamical capital market. This paper tentatively analyzes the cross-development between EMH and FMH, as well as the application and tendency of FMH. We firstly clarificate that FMH is not a substitution or alternative but a complement to EMH, and reveal that the intrinsic unity is their essential relationship. Then we emphasize repeatedly that studies of domestic mostly remain at initial stage. There have been too many empirical analyses to demonstrate the fractal structure of market, but relatively too little work of what the microscopic causes are or how to conduct portfolio selection and risk management according to FMH. Our basic discussion is supposed to conclude the logicality between different theories and application prospects of FMH. We hope cautiously that our personal views could inspire some guidance for further research.","PeriodicalId":354870,"journal":{"name":"2012 Fifth International Workshop on Chaos-fractals Theories and Applications","volume":"308 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121292294","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}
Z. Zhiliang, Liu Sha, Zhang Jiawei, Zhao Yuli, Yu Hai
Degree distribution lies at the heart of design an LT code. It affects the encoding and decoding complexity and error performance of LT code. In this paper, some metrics of well-design LT code such as average degree, release probability, overhead factor is analyzed. It will compare the metrics among robust LT code, sub optimal LT code and SF-LT code. Moreover, it provides some mathematical guideline on how to design a well designed LT code.
{"title":"Performance Analysis of LT Codes with Different Degree Distribution","authors":"Z. Zhiliang, Liu Sha, Zhang Jiawei, Zhao Yuli, Yu Hai","doi":"10.1109/IWCFTA.2012.39","DOIUrl":"https://doi.org/10.1109/IWCFTA.2012.39","url":null,"abstract":"Degree distribution lies at the heart of design an LT code. It affects the encoding and decoding complexity and error performance of LT code. In this paper, some metrics of well-design LT code such as average degree, release probability, overhead factor is analyzed. It will compare the metrics among robust LT code, sub optimal LT code and SF-LT code. Moreover, it provides some mathematical guideline on how to design a well designed LT code.","PeriodicalId":354870,"journal":{"name":"2012 Fifth International Workshop on Chaos-fractals Theories and Applications","volume":"501 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123062188","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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