The Experts below are selected from a list of 104889 Experts worldwide ranked by ideXlab platform
Viet-thanh Pham - One of the best experts on this subject based on the ideXlab platform.
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A New Chaotic System with Stable Equilibrium: Entropy Analysis, Parameter Estimation, and Circuit Design
Entropy, 2018Co-Authors: Tomasz Kapitaniak, Tasawar Hayat, S. Alireza Mohammadi, Saad Mekhilef, Fawaz E. Alsaadi, Viet-thanh PhamAbstract:In this paper, we introduce a new, three-dimensional chaotic system with one Stable Equilibrium. This system is a multiStable dynamic system in which the strange attractor is hidden. We investigate its dynamic properties through Equilibrium analysis, a bifurcation diagram and Lyapunov exponents. Such multiStable systems are important in engineering. We perform an entropy analysis, parameter estimation and circuit design using this new system to show its feasibility and ability to be used in engineering applications.
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A new three-dimensional chaotic flow with one Stable Equilibrium: dynamical properties and complexity analysis
Open Physics, 2018Co-Authors: Abdul Jalil M. Khalaf, Tomasz Kapitaniak, Karthikeyan Rajagopal, Ahmed Alsaedi, Tasawar Hayat, Viet-thanh PhamAbstract:Abstract This paper proposes a new three-dimensional chaotic flow with one Stable Equilibrium. Dynamical properties of this system are investigated. The system has a chaotic attractor coexisting with a Stable Equilibrium. Thus the chaotic attractor is hidden. Basin of attractions shows the tangle of different attractors. Also, some complexity measures of the system such as Lyapunov exponent and entropy will are analyzed. We show that the Kolmogorov-Sinai Entropy shows more accurate results in comparison with Shanon Entropy.
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A Chaotic System with Two Stable Equilibrium Points: Dynamics, Circuit Realization and Communication Application
International Journal of Bifurcation and Chaos, 2017Co-Authors: Xiong Wang, Viet-thanh Pham, Akif Akgul, Serdar Çiçek, Duy Vo HoangAbstract:Recent evidence suggests that a system with only Stable equilibria can generate chaotic behavior. In this work, we study a chaotic system with two Stable Equilibrium points. The dynamics of the system is investigated via phase portrait, bifurcation diagram and Lyapunov exponents. The feasibility of the system is introducing its electronic realization. Moreover, the chaotic system is used in Symmetric Chaos Shift Keying (SCSK) and Chaotic ON-OFF Keying (COOK) modulated communication designs for secure communication. It is determined that the SCSK modulated communication system implemented with the chaotic system is more successful than COOK modulation for secure communication.
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From Wang–Chen System with Only One Stable Equilibrium to a New Chaotic System Without Equilibrium
International Journal of Bifurcation and Chaos, 2017Co-Authors: Viet-thanh Pham, Sajad Jafari, Christos Volos, Xiong Wang, Tomasz KapitaniakAbstract:Wang–Chen system with only one Stable Equilibrium as well as the coexistence of hidden attractors has attracted increasing interest due to its striking features. In this work, the effect of state feedback on Wang–Chen system is investigated by introducing a further state variable. It is worth noting that a new chaotic system without Equilibrium is obtained. We believe that the system is an interesting example to illustrate the conversion of hidden attractors with one Stable Equilibrium to hidden attractors without Equilibrium.
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from wang chen system with only one Stable Equilibrium to a new chaotic system without Equilibrium
International Journal of Bifurcation and Chaos, 2017Co-Authors: Sajad Jafari, Viet-thanh Pham, Christos Volos, Xiong Wang, Tomasz KapitaniakAbstract:Wang–Chen system with only one Stable Equilibrium as well as the coexistence of hidden attractors has attracted increasing interest due to its striking features. In this work, the effect of state feedback on Wang–Chen system is investigated by introducing a further state variable. It is worth noting that a new chaotic system without Equilibrium is obtained. We believe that the system is an interesting example to illustrate the conversion of hidden attractors with one Stable Equilibrium to hidden attractors without Equilibrium.
Tomasz Kapitaniak - One of the best experts on this subject based on the ideXlab platform.
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A New Chaotic System with Stable Equilibrium: Entropy Analysis, Parameter Estimation, and Circuit Design
Entropy, 2018Co-Authors: Tomasz Kapitaniak, Tasawar Hayat, S. Alireza Mohammadi, Saad Mekhilef, Fawaz E. Alsaadi, Viet-thanh PhamAbstract:In this paper, we introduce a new, three-dimensional chaotic system with one Stable Equilibrium. This system is a multiStable dynamic system in which the strange attractor is hidden. We investigate its dynamic properties through Equilibrium analysis, a bifurcation diagram and Lyapunov exponents. Such multiStable systems are important in engineering. We perform an entropy analysis, parameter estimation and circuit design using this new system to show its feasibility and ability to be used in engineering applications.
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A new three-dimensional chaotic flow with one Stable Equilibrium: dynamical properties and complexity analysis
Open Physics, 2018Co-Authors: Abdul Jalil M. Khalaf, Tomasz Kapitaniak, Karthikeyan Rajagopal, Ahmed Alsaedi, Tasawar Hayat, Viet-thanh PhamAbstract:Abstract This paper proposes a new three-dimensional chaotic flow with one Stable Equilibrium. Dynamical properties of this system are investigated. The system has a chaotic attractor coexisting with a Stable Equilibrium. Thus the chaotic attractor is hidden. Basin of attractions shows the tangle of different attractors. Also, some complexity measures of the system such as Lyapunov exponent and entropy will are analyzed. We show that the Kolmogorov-Sinai Entropy shows more accurate results in comparison with Shanon Entropy.
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From Wang–Chen System with Only One Stable Equilibrium to a New Chaotic System Without Equilibrium
International Journal of Bifurcation and Chaos, 2017Co-Authors: Viet-thanh Pham, Sajad Jafari, Christos Volos, Xiong Wang, Tomasz KapitaniakAbstract:Wang–Chen system with only one Stable Equilibrium as well as the coexistence of hidden attractors has attracted increasing interest due to its striking features. In this work, the effect of state feedback on Wang–Chen system is investigated by introducing a further state variable. It is worth noting that a new chaotic system without Equilibrium is obtained. We believe that the system is an interesting example to illustrate the conversion of hidden attractors with one Stable Equilibrium to hidden attractors without Equilibrium.
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from wang chen system with only one Stable Equilibrium to a new chaotic system without Equilibrium
International Journal of Bifurcation and Chaos, 2017Co-Authors: Sajad Jafari, Viet-thanh Pham, Christos Volos, Xiong Wang, Tomasz KapitaniakAbstract:Wang–Chen system with only one Stable Equilibrium as well as the coexistence of hidden attractors has attracted increasing interest due to its striking features. In this work, the effect of state feedback on Wang–Chen system is investigated by introducing a further state variable. It is worth noting that a new chaotic system without Equilibrium is obtained. We believe that the system is an interesting example to illustrate the conversion of hidden attractors with one Stable Equilibrium to hidden attractors without Equilibrium.
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Generating a Chaotic System with One Stable Equilibrium
International Journal of Bifurcation and Chaos, 2017Co-Authors: Viet-thanh Pham, Sajad Jafari, Tomasz Kapitaniak, Christos Volos, Sifeu Takougang KingniAbstract:Although chaotic systems with hidden attractors have been discovered recently, there are few investigations about relationships among them. This brief work introduces a novel chaotic system with only one Stable Equilibrium that is constructed by adding a tiny perturbation into a known chaotic flow having hidden attractors with a line Equilibrium.
Xiong Wang - One of the best experts on this subject based on the ideXlab platform.
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A Chaotic System with Two Stable Equilibrium Points: Dynamics, Circuit Realization and Communication Application
International Journal of Bifurcation and Chaos, 2017Co-Authors: Xiong Wang, Viet-thanh Pham, Akif Akgul, Serdar Çiçek, Duy Vo HoangAbstract:Recent evidence suggests that a system with only Stable equilibria can generate chaotic behavior. In this work, we study a chaotic system with two Stable Equilibrium points. The dynamics of the system is investigated via phase portrait, bifurcation diagram and Lyapunov exponents. The feasibility of the system is introducing its electronic realization. Moreover, the chaotic system is used in Symmetric Chaos Shift Keying (SCSK) and Chaotic ON-OFF Keying (COOK) modulated communication designs for secure communication. It is determined that the SCSK modulated communication system implemented with the chaotic system is more successful than COOK modulation for secure communication.
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From Wang–Chen System with Only One Stable Equilibrium to a New Chaotic System Without Equilibrium
International Journal of Bifurcation and Chaos, 2017Co-Authors: Viet-thanh Pham, Sajad Jafari, Christos Volos, Xiong Wang, Tomasz KapitaniakAbstract:Wang–Chen system with only one Stable Equilibrium as well as the coexistence of hidden attractors has attracted increasing interest due to its striking features. In this work, the effect of state feedback on Wang–Chen system is investigated by introducing a further state variable. It is worth noting that a new chaotic system without Equilibrium is obtained. We believe that the system is an interesting example to illustrate the conversion of hidden attractors with one Stable Equilibrium to hidden attractors without Equilibrium.
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from wang chen system with only one Stable Equilibrium to a new chaotic system without Equilibrium
International Journal of Bifurcation and Chaos, 2017Co-Authors: Sajad Jafari, Viet-thanh Pham, Christos Volos, Xiong Wang, Tomasz KapitaniakAbstract:Wang–Chen system with only one Stable Equilibrium as well as the coexistence of hidden attractors has attracted increasing interest due to its striking features. In this work, the effect of state feedback on Wang–Chen system is investigated by introducing a further state variable. It is worth noting that a new chaotic system without Equilibrium is obtained. We believe that the system is an interesting example to illustrate the conversion of hidden attractors with one Stable Equilibrium to hidden attractors without Equilibrium.
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A New Chaotic System With Stable Equilibrium: From Theoretical Model to Circuit Implementation
IEEE Access, 2017Co-Authors: Xiong Wang, Sajad Jafari, Viet-thanh Pham, Christos Volos, Jesus M. Munoz-pacheco, Esteban Tlelo-cuautleAbstract:Recent evidences suggest that complex behavior such as chaos can be observed in a nonlinear system with Stable equilibria. However, few studies have investigated chaotic systems with only one Stable Equilibrium. This paper introduces a new 3-D chaotic system having only one Stable Equilibrium. Dynamics of the new system are discovered by using phase portraits, basin of attraction, bifurcation diagram, and maximal Lyapunov exponents. It is interesting that the system has a state variable related with the freedom of offset boosting. In addition, we have investigated the anti-synchronization of the system via an adaptive control. Furthermore, the feasibility of the system is also discussed through presenting its electronic circuit implementation.
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A chaotic system with only one Stable Equilibrium
Communications in Nonlinear Science and Numerical Simulation, 2012Co-Authors: Xiong Wang, Guanrong ChenAbstract:Abstract If you are given a simple three-dimensional autonomous quadratic system that has only one Stable Equilibrium, what would you predict its dynamics to be, Stable or periodic? Will it be surprising if you are shown that such a system is actually chaotic? Although chaos theory for three-dimensional autonomous systems has been intensively and extensively studied since the time of Lorenz in the 1960s, and the theory has become quite mature today, it seems that no one would anticipate a possibility of finding a three-dimensional autonomous quadratic chaotic system with only one Stable Equilibrium. The discovery of the new system, to be reported in this Letter, is indeed striking because for a three-dimensional autonomous quadratic system with a single Stable node-focus Equilibrium, one typically would anticipate non-chaotic and even asymptotically converging behaviors. Although the Equilibrium is changed from an unStable saddle-focus to a Stable node-focus, therefore the familiar Si’lnikov homoclinic criterion is not applicable, it is demonstrated to be chaotic in the sense of having a positive largest Lyapunov exponent, a fractional dimension, a continuous broad frequency spectrum, and a period-doubling route to chaos.
Hanhua Zhu - One of the best experts on this subject based on the ideXlab platform.
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Engineering Structure-Related Stable Equilibrium and Deformation Compatibility Control Method
Deformation Compatibility Control for Engineering Structures, 2016Co-Authors: Hanhua Zhu, Zhihui Zhou, Mengchong Chen, Jianliang DengAbstract:Engineering techniques are a combination of scientific techniques composed of theory analysis, statistical induction, analogical summarization, as well as tests and verifications. Therefore, engineering structure-related Stable Equilibrium problems not only require theory analysis, but also necessitate comprehensive revision and continuous improvements by using applied statistics, analogy, and tests. We first conducted an overall statistical analysis of over 40,000 engineering cases that satisfy Stable Equilibrium conditions.
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Key Techniques of Underground Engineering Stable Equilibrium Theory
Stability Assessment for Underground Excavations and Key Construction Techniques, 2016Co-Authors: Hanhua Zhu, Yu ZhaoAbstract:Given the current productive efficiency in China, the core of design method is to “basically maintain the original status of strata (surrounding rock)”, so as to achieve the goal of “reasonably exerting the self-bearing capacity of strata (surrounding rock). In another word, the interaction between strata (surrounding rock) and supporting structure will help the system to achieve the “Stable Equilibrium and deformation compatibility control”. The design theories and construction methods are in consistency in this concern. The underground engineering Stable Equilibrium theory not only provides the elaboration of mechanics theory but also requirements for construction methods. The theory describes the basic concept of underground structure design and construction, the suitability and consistency of different design theories and construction methods in a better way. In addition, it also emphasize the significance of underground structure design details and reasonable construction process, which reflects the concept of “simplifying complicated issues”. In Timo Shenko mechanics theory, the complicated boundary condition mechanics issues are simplified before solved, in order to better understand the physical interpretation of engineering problems, and thus facilitate the underground engineering design and construction. Based on the underground engineering Stable Equilibrium theory, four construction techniques are provided and illustrated with cases in this chapter.
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Formation and Development of Underground Engineering Stable Equilibrium Theory
Stability Assessment for Underground Excavations and Key Construction Techniques, 2016Co-Authors: Hanhua Zhu, Yu ZhaoAbstract:The underground engineering surrounding rock exists in certain geological environment, and is vulnerable to influences of tectonic and weathering process. The discontinuities formed inside the surrounding rock intersect the complete rock mass into rock blocks of different shapes and sizes. Before starting underground excavation, the rock mass is in a Stable Equilibrium status. Excavation will cause unload rebound deformation and stress redistribution on the surrounding rock. If the strength of surrounding rock is stronger than the redistributed stress action after excavation, the surrounding rock will not be obviously deformed or damaged. In this case, no supporting is needed, or only localized supporting is enough to maintain the stability of surrounding rock. If the strength of the surrounding rock is weaker than the redistributed stress action, the surrounding rock may be drastically deformed, which may result in instability and failure. In such a case, strong pre-reinforcement measures should be taken to ensure that the proper interaction of the surrounding rock and supporting structure meets the Stable Equilibrium and deformation compatibility control requirements, and thus truly “reasonably exert the self-bearing capacity of surrounding rock”. In this chapter, the advantages and disadvantage of traditional load theories (loose load theory and rock bearing theory) were summarized and discussed. The physical significance of Stable Equilibrium and deformation compatibility control was interpreted using a simple ball-ropes model. Then these concepts were introduced into underground engineering.
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Application of Stable Equilibrium Theory to Metro Tunnels and River-Crossing Tunnels Using Shield Tunneling Method
Stability Assessment for Underground Excavations and Key Construction Techniques, 2016Co-Authors: Hanhua Zhu, Mengchong ChenAbstract:The expansion of cities and increase of the population leads to heavy traffic which, in town, causes air pollution and traffic jam. These belong to the most important problems in nowadays urbanization. The metro tunnels and is considered as an efficient medium of public transportation and is widely used to alleviate traffic problems and environmental pollution. Since many developed cities have rivers crossed through, tunneling shields sometimes have to cross rivers. The tunneling inevitably caused ground subsidence and consequently influence on the buildings and river banks [1]. It is necessary to utilize the Stable Equilibrium theory and related techniques to control the ground subsidence and its negative impact within an allowed limit. This chapter illustrated the application of the theory with two such cases.
Sajad Jafari - One of the best experts on this subject based on the ideXlab platform.
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From Wang–Chen System with Only One Stable Equilibrium to a New Chaotic System Without Equilibrium
International Journal of Bifurcation and Chaos, 2017Co-Authors: Viet-thanh Pham, Sajad Jafari, Christos Volos, Xiong Wang, Tomasz KapitaniakAbstract:Wang–Chen system with only one Stable Equilibrium as well as the coexistence of hidden attractors has attracted increasing interest due to its striking features. In this work, the effect of state feedback on Wang–Chen system is investigated by introducing a further state variable. It is worth noting that a new chaotic system without Equilibrium is obtained. We believe that the system is an interesting example to illustrate the conversion of hidden attractors with one Stable Equilibrium to hidden attractors without Equilibrium.
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from wang chen system with only one Stable Equilibrium to a new chaotic system without Equilibrium
International Journal of Bifurcation and Chaos, 2017Co-Authors: Sajad Jafari, Viet-thanh Pham, Christos Volos, Xiong Wang, Tomasz KapitaniakAbstract:Wang–Chen system with only one Stable Equilibrium as well as the coexistence of hidden attractors has attracted increasing interest due to its striking features. In this work, the effect of state feedback on Wang–Chen system is investigated by introducing a further state variable. It is worth noting that a new chaotic system without Equilibrium is obtained. We believe that the system is an interesting example to illustrate the conversion of hidden attractors with one Stable Equilibrium to hidden attractors without Equilibrium.
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Generating a Chaotic System with One Stable Equilibrium
International Journal of Bifurcation and Chaos, 2017Co-Authors: Viet-thanh Pham, Sajad Jafari, Tomasz Kapitaniak, Christos Volos, Sifeu Takougang KingniAbstract:Although chaotic systems with hidden attractors have been discovered recently, there are few investigations about relationships among them. This brief work introduces a novel chaotic system with only one Stable Equilibrium that is constructed by adding a tiny perturbation into a known chaotic flow having hidden attractors with a line Equilibrium.
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A New Chaotic System With Stable Equilibrium: From Theoretical Model to Circuit Implementation
IEEE Access, 2017Co-Authors: Xiong Wang, Sajad Jafari, Viet-thanh Pham, Christos Volos, Jesus M. Munoz-pacheco, Esteban Tlelo-cuautleAbstract:Recent evidences suggest that complex behavior such as chaos can be observed in a nonlinear system with Stable equilibria. However, few studies have investigated chaotic systems with only one Stable Equilibrium. This paper introduces a new 3-D chaotic system having only one Stable Equilibrium. Dynamics of the new system are discovered by using phase portraits, basin of attraction, bifurcation diagram, and maximal Lyapunov exponents. It is interesting that the system has a state variable related with the freedom of offset boosting. In addition, we have investigated the anti-synchronization of the system via an adaptive control. Furthermore, the feasibility of the system is also discussed through presenting its electronic circuit implementation.
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three dimensional chaotic autonomous system with only one Stable Equilibrium analysis circuit design parameter estimation control synchronization and its fractional order form
European Physical Journal Plus, 2014Co-Authors: Sifeu Takougang Kingni, Hermann Simo, Sajad Jafari, Paul WoafoAbstract:This paper proposes a three-dimensional chaotic autonomous system with only one Stable Equilibrium. This system belongs to a newly introduced category of chaotic systems with hidden attractors. The nonlinear dynamics of the proposed chaotic system is described through numerical simulations which include phase portraits, bifurcation diagrams and new cost function for parameter estimation of chaotic flows. The coexistence of a Stable Equilibrium point with a strange attractor is found in the proposed system for specific parameters values. The physical existence of the chaotic behavior found in the proposed system is verified by using the Orcard-PSpice software. A good qualitative agreement is shown between the simulations and the experimental results. Based on the Routh-Hurwitz conditions and for a specific choice of linear controllers, it is shown that the proposed chaotic system is controlled to its Equilibrium point. Chaos synchronization of an identical proposed system is achieved by using the unidirectional linear and nonlinear error feedback coupling. Finally, the fractional-order form of the proposed system is studied by using the stability theory of fractional-order systems and numerical simulations. A necessary condition for the commensurate fractional order of this system to remain chaotic is obtained. It is found that chaos exists in this system with order less than three.
