The Experts below are selected from a list of 9357 Experts worldwide ranked by ideXlab platform
Conrad Bertrand Tabi - One of the best experts on this subject based on the ideXlab platform.
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dynamical analysis of the fitzhugh nagumo oscillations through a modified van der pol equation with Fractional Order Derivative term
International Journal of Non-linear Mechanics, 2018Co-Authors: Conrad Bertrand TabiAbstract:Abstract The nonlinear dynamics of action potentials in the FitzHugh–Nagumo model is addressed using a modified Van der Pol equation with Fractional-Order Derivative and periodic parametric excitation. Through the averaging method, the approximately analytical and the steady-state solutions are obtained, and their existence condition and stability are investigated. Analytical calculations are confirmed numerically and one insists on the coupled effects of the parametric excitation, system parameters and Fractional-Order parameter to discuss the various dynamical behaviors of the studied system. Mainly, the Fractional-Order Derivative modifies the features of the amplitude–frequency curves. This might be an efficient tool to control the dynamics of the action potentials, with important biological implications that are discussed.
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Dynamical analysis of the FitzHugh–Nagumo oscillations through a modified Van der Pol equation with Fractional-Order Derivative term
International Journal of Non-Linear Mechanics, 2018Co-Authors: Conrad Bertrand TabiAbstract:Abstract The nonlinear dynamics of action potentials in the FitzHugh–Nagumo model is addressed using a modified Van der Pol equation with Fractional-Order Derivative and periodic parametric excitation. Through the averaging method, the approximately analytical and the steady-state solutions are obtained, and their existence condition and stability are investigated. Analytical calculations are confirmed numerically and one insists on the coupled effects of the parametric excitation, system parameters and Fractional-Order parameter to discuss the various dynamical behaviors of the studied system. Mainly, the Fractional-Order Derivative modifies the features of the amplitude–frequency curves. This might be an efficient tool to control the dynamics of the action potentials, with important biological implications that are discussed.
Shaopu Yang - One of the best experts on this subject based on the ideXlab platform.
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Dynamic response of a piecewise linear single-degree-of-freedom oscillator with Fractional-Order Derivative:
Journal of Low Frequency Noise Vibration and Active Control, 2019Co-Authors: Jun Wang, Shaopu Yang, Yongjun Shen, Dawei ZuoAbstract:In this paper, the dynamic response of a piecewise linear single-degree-of-freedom oscillator with Fractional-Order Derivative is studied. First, a mathematical model of the single-degree-of-freedo...
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Chaos detection of Duffing system with Fractional-Order Derivative by Melnikov method.
Chaos (Woodbury N.Y.), 2019Co-Authors: Jiangchuan Niu, Yongjun Shen, Ruyu Liu, Shaopu YangAbstract:The chaos detection of the Duffing system with the Fractional-Order Derivative subjected to external harmonic excitation is investigated by the Melnikov method. In Order to apply the Melnikov method to detect the chaos of the Duffing system with the Fractional-Order Derivative, it is transformed into the first-Order approximate equivalent integer-Order system via the harmonic balance method, which has the same steady-state amplitude-frequency response equation with the original system. Also, the amplitude-frequency response of the Duffing system with the Fractional-Order Derivative and its first-Order approximate equivalent integer-Order system are compared by the numerical solutions, and they are in good agreement. Then, the analytical chaos criterion of the Duffing system with the Fractional-Order Derivative is obtained by the Melnikov function. The bifurcation and chaos of the Duffing system with the Fractional-Order Derivative and an integer-Order Derivative are analyzed in detail, and the chaos criterion obtained by the Melnikov function is verified by using bifurcation analysis and phase portraits. The analysis results show that the Melnikov method is effective to detect the chaos in the Duffing system with the Fractional-Order Derivative by transforming it into an equivalent integer-Order system.
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Dynamical Analysis on Single Degree-of-Freedom Semiactive Control System by Using Fractional-Order Derivative
Mathematical Problems in Engineering, 2015Co-Authors: Yongjun Shen, Shaopu Yang, Minghui Fan, Xing HaijunAbstract:The single degree-of-freedom (SDOF) system under the control of three semiactive methods is analytically studied in this paper, where a Fractional-Order Derivative is used in the mathematical model. The three semiactive control methods are on-off control, limited relative displacement (LRD) control, and relative control, respectively. The averaging method is adopted to provide an analytical study on the performance of the three different control methods. Based on the comparison between the analytical solutions with the numerical ones, it could be proved that the analytical solutions are accurate enough. The effects of the Fractional-Order parameters on the control performance, especially the relative and absolute displacement transmissibility, are analyzed. The research results indicate that the steady-state amplitudes of the three semiactive systems with Fractional-Order Derivative in the model could be significantly reduced and the control performance can be greatly improved.
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Primary resonance of Fractional-Order van der Pol oscillator
Nonlinear Dynamics, 2014Co-Authors: Yongjun Shen, Peng Wei, Shaopu YangAbstract:In this paper the primary resonance of van der Pol (VDP) oscillator with Fractional-Order Derivative is studied analytically and numerically. At first the approximately analytical solution is obtained by the averaging method, and it is found that the Fractional-Order Derivative could affect the dynamical properties of VDP oscillator, which is characterized by the equivalent damping coefficient and the equivalent stiffness coefficient. Moreover, the amplitude–frequency equation for steady-state solution is established, and the corresponding stability condition is also presented based on Lyapunov theory. Then, the comparisons of several different amplitude–frequency curves by the approximately analytical solution and the numerical integration are fulfilled, and the results certify the correctness and satisfactory precision of the approximately analytical solution. At last, the effects of the two Fractional parameters, i.e., the Fractional coefficient and the Fractional Order, on the amplitude–frequency curves are investigated for some typical excitation amplitudes, which are different from the traditional integer-Order VDP oscillator.
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Subharmonic Resonance of Van Der Pol Oscillator with Fractional-Order Derivative
Mathematical Problems in Engineering, 2014Co-Authors: Yongjun Shen, Peng Wei, Chuanyi Sui, Shaopu YangAbstract:The subharmonic resonance of van der Pol (VDP) oscillator with Fractional-Order Derivative is studied by the averaging method. At first, the first-Order approximate solutions are obtained by the averaging method. Then the definitions of equivalent linear damping coefficient (ELDC) and equivalent linear stiffness coefficient (ELSC) for subharmonic resonance are established, and the effects of the Fractional-Order parameters on the ELDC, the ELSC, and the dynamical characteristics of system are also analysed. Moreover, the amplitude-frequency equation and phase-frequency equation of steady-state solution for subharmonic resonance are established. The corresponding stability condition is presented based on Lyapunov theory, and the existence condition for subharmonic resonance (ECSR) is also obtained. At last, the comparisons of the Fractional-Order and the traditional integer-Order VDP oscillator are fulfilled by the numerical simulation. The effects of the parameters in Fractional-Order Derivative on the steady-state amplitude, the amplitude-frequency curves, and the system stability are also studied.
Yongjun Shen - One of the best experts on this subject based on the ideXlab platform.
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Dynamic response of a piecewise linear single-degree-of-freedom oscillator with Fractional-Order Derivative:
Journal of Low Frequency Noise Vibration and Active Control, 2019Co-Authors: Jun Wang, Shaopu Yang, Yongjun Shen, Dawei ZuoAbstract:In this paper, the dynamic response of a piecewise linear single-degree-of-freedom oscillator with Fractional-Order Derivative is studied. First, a mathematical model of the single-degree-of-freedo...
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Chaos detection of Duffing system with Fractional-Order Derivative by Melnikov method.
Chaos (Woodbury N.Y.), 2019Co-Authors: Jiangchuan Niu, Yongjun Shen, Ruyu Liu, Shaopu YangAbstract:The chaos detection of the Duffing system with the Fractional-Order Derivative subjected to external harmonic excitation is investigated by the Melnikov method. In Order to apply the Melnikov method to detect the chaos of the Duffing system with the Fractional-Order Derivative, it is transformed into the first-Order approximate equivalent integer-Order system via the harmonic balance method, which has the same steady-state amplitude-frequency response equation with the original system. Also, the amplitude-frequency response of the Duffing system with the Fractional-Order Derivative and its first-Order approximate equivalent integer-Order system are compared by the numerical solutions, and they are in good agreement. Then, the analytical chaos criterion of the Duffing system with the Fractional-Order Derivative is obtained by the Melnikov function. The bifurcation and chaos of the Duffing system with the Fractional-Order Derivative and an integer-Order Derivative are analyzed in detail, and the chaos criterion obtained by the Melnikov function is verified by using bifurcation analysis and phase portraits. The analysis results show that the Melnikov method is effective to detect the chaos in the Duffing system with the Fractional-Order Derivative by transforming it into an equivalent integer-Order system.
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Dynamical Analysis on Single Degree-of-Freedom Semiactive Control System by Using Fractional-Order Derivative
Mathematical Problems in Engineering, 2015Co-Authors: Yongjun Shen, Shaopu Yang, Minghui Fan, Xing HaijunAbstract:The single degree-of-freedom (SDOF) system under the control of three semiactive methods is analytically studied in this paper, where a Fractional-Order Derivative is used in the mathematical model. The three semiactive control methods are on-off control, limited relative displacement (LRD) control, and relative control, respectively. The averaging method is adopted to provide an analytical study on the performance of the three different control methods. Based on the comparison between the analytical solutions with the numerical ones, it could be proved that the analytical solutions are accurate enough. The effects of the Fractional-Order parameters on the control performance, especially the relative and absolute displacement transmissibility, are analyzed. The research results indicate that the steady-state amplitudes of the three semiactive systems with Fractional-Order Derivative in the model could be significantly reduced and the control performance can be greatly improved.
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Primary resonance of Fractional-Order van der Pol oscillator
Nonlinear Dynamics, 2014Co-Authors: Yongjun Shen, Peng Wei, Shaopu YangAbstract:In this paper the primary resonance of van der Pol (VDP) oscillator with Fractional-Order Derivative is studied analytically and numerically. At first the approximately analytical solution is obtained by the averaging method, and it is found that the Fractional-Order Derivative could affect the dynamical properties of VDP oscillator, which is characterized by the equivalent damping coefficient and the equivalent stiffness coefficient. Moreover, the amplitude–frequency equation for steady-state solution is established, and the corresponding stability condition is also presented based on Lyapunov theory. Then, the comparisons of several different amplitude–frequency curves by the approximately analytical solution and the numerical integration are fulfilled, and the results certify the correctness and satisfactory precision of the approximately analytical solution. At last, the effects of the two Fractional parameters, i.e., the Fractional coefficient and the Fractional Order, on the amplitude–frequency curves are investigated for some typical excitation amplitudes, which are different from the traditional integer-Order VDP oscillator.
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Subharmonic Resonance of Van Der Pol Oscillator with Fractional-Order Derivative
Mathematical Problems in Engineering, 2014Co-Authors: Yongjun Shen, Peng Wei, Chuanyi Sui, Shaopu YangAbstract:The subharmonic resonance of van der Pol (VDP) oscillator with Fractional-Order Derivative is studied by the averaging method. At first, the first-Order approximate solutions are obtained by the averaging method. Then the definitions of equivalent linear damping coefficient (ELDC) and equivalent linear stiffness coefficient (ELSC) for subharmonic resonance are established, and the effects of the Fractional-Order parameters on the ELDC, the ELSC, and the dynamical characteristics of system are also analysed. Moreover, the amplitude-frequency equation and phase-frequency equation of steady-state solution for subharmonic resonance are established. The corresponding stability condition is presented based on Lyapunov theory, and the existence condition for subharmonic resonance (ECSR) is also obtained. At last, the comparisons of the Fractional-Order and the traditional integer-Order VDP oscillator are fulfilled by the numerical simulation. The effects of the parameters in Fractional-Order Derivative on the steady-state amplitude, the amplitude-frequency curves, and the system stability are also studied.
Derek P. Atherton - One of the best experts on this subject based on the ideXlab platform.
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an integer Order approximation method based on stability boundary locus for Fractional Order Derivative integrator operators
Isa Transactions, 2016Co-Authors: Furkan Nur Deniz, Nusret Tan, Baris Baykant Alagoz, Derek P. AthertonAbstract:This paper introduces an integer Order approximation method for numerical implementation of Fractional Order Derivative/integrator operators in control systems. The proposed method is based on fitting the stability boundary locus (SBL) of Fractional Order Derivative/integrator operators and SBL of integer Order transfer functions. SBL defines a boundary in the parametric design plane of controller, which separates stable and unstable regions of a feedback control system and SBL analysis is mainly employed to graphically indicate the choice of controller parameters which result in stable operation of the feedback systems. This study reveals that the SBL curves of Fractional Order operators can be matched with integer Order models in a limited frequency range. SBL fitting method provides straightforward solutions to obtain an integer Order model approximation of Fractional Order operators and systems according to matching points from SBL of Fractional Order systems in desired frequency ranges. Thus, the proposed method can effectively deal with stability preservation problems of approximate models. Illustrative examples are given to show performance of the proposed method and results are compared with the well-known approximation methods developed for Fractional Order systems. The integer-Order approximate modeling of Fractional Order PID controllers is also illustrated for control applications.
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An integer Order approximation method based on stability boundary locus for Fractional Order Derivative/integrator operators
Isa Transactions, 2016Co-Authors: Furkan Nur Deniz, Baris Baykant Alagoz, Derek P. AthertonAbstract:This paper introduces an integer Order approximation method for numerical implementation of Fractional Order Derivative/integrator operators in control systems. The proposed method is based on fitting the stability boundary locus (SBL) of Fractional Order Derivative/integrator operators and SBL of integer Order transfer functions. SBL defines a boundary in the parametric design plane of controller, which separates stable and unstable regions of a feedback control system and SBL analysis is mainly employed to graphically indicate the choice of controller parameters which result in stable operation of the feedback systems. This study reveals that the SBL curves of Fractional Order operators can be matched with integer Order models in a limited frequency range. SBL fitting method provides straightforward solutions to obtain an integer Order model approximation of Fractional Order operators and systems according to matching points from SBL of Fractional Order systems in desired frequency ranges. Thus, the proposed method can effectively deal with stability preservation problems of approximate models. Illustrative examples are given to show performance of the proposed method and results are compared with the well-known approximation methods developed for Fractional Order systems. The integer-Order approximate modeling of Fractional Order PID controllers is also illustrated for control applications.
Peng Wei - One of the best experts on this subject based on the ideXlab platform.
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Primary resonance of Fractional-Order van der Pol oscillator
Nonlinear Dynamics, 2014Co-Authors: Yongjun Shen, Peng Wei, Shaopu YangAbstract:In this paper the primary resonance of van der Pol (VDP) oscillator with Fractional-Order Derivative is studied analytically and numerically. At first the approximately analytical solution is obtained by the averaging method, and it is found that the Fractional-Order Derivative could affect the dynamical properties of VDP oscillator, which is characterized by the equivalent damping coefficient and the equivalent stiffness coefficient. Moreover, the amplitude–frequency equation for steady-state solution is established, and the corresponding stability condition is also presented based on Lyapunov theory. Then, the comparisons of several different amplitude–frequency curves by the approximately analytical solution and the numerical integration are fulfilled, and the results certify the correctness and satisfactory precision of the approximately analytical solution. At last, the effects of the two Fractional parameters, i.e., the Fractional coefficient and the Fractional Order, on the amplitude–frequency curves are investigated for some typical excitation amplitudes, which are different from the traditional integer-Order VDP oscillator.
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Subharmonic Resonance of Van Der Pol Oscillator with Fractional-Order Derivative
Mathematical Problems in Engineering, 2014Co-Authors: Yongjun Shen, Peng Wei, Chuanyi Sui, Shaopu YangAbstract:The subharmonic resonance of van der Pol (VDP) oscillator with Fractional-Order Derivative is studied by the averaging method. At first, the first-Order approximate solutions are obtained by the averaging method. Then the definitions of equivalent linear damping coefficient (ELDC) and equivalent linear stiffness coefficient (ELSC) for subharmonic resonance are established, and the effects of the Fractional-Order parameters on the ELDC, the ELSC, and the dynamical characteristics of system are also analysed. Moreover, the amplitude-frequency equation and phase-frequency equation of steady-state solution for subharmonic resonance are established. The corresponding stability condition is presented based on Lyapunov theory, and the existence condition for subharmonic resonance (ECSR) is also obtained. At last, the comparisons of the Fractional-Order and the traditional integer-Order VDP oscillator are fulfilled by the numerical simulation. The effects of the parameters in Fractional-Order Derivative on the steady-state amplitude, the amplitude-frequency curves, and the system stability are also studied.
