scholarly journals Characteristic Analysis of Fractional-Order Memristor-Based Hypogenetic Jerk System and Its DSP Implementation

Electronics ◽  
2021 ◽  
Vol 10 (7) ◽  
pp. 841
Author(s):  
Chuan Qin ◽  
Kehui Sun ◽  
Shaobo He
Keyword(s):  
Lyapunov Exponent ◽  
Fractional Order ◽  
Digital Signal Processor ◽  
Adomian Decomposition Method ◽  
Digital Signal ◽  
Maximum Lyapunov Exponent ◽  
Characteristic Analysis ◽  
Coexisting Attractors ◽  
Dsp Implementation ◽  
Adomian Decomposition

In this paper, a fractional-order memristive model with infinite coexisting attractors is investigated. The numerical solution of the system is derived based on the Adomian decomposition method (ADM), and its dynamic behaviors are analyzed by means of phase diagrams, bifurcation diagrams, Lyapunov exponent spectrum (LEs), dynamic map based on SE complexity and maximum Lyapunov exponent (MLE). Simulation results show that it has rich dynamic characteristics, including asymmetric coexisting attractors with different structures and offset boosting. Finally, the digital signal processor (DSP) implementation verifies the correctness of the solution algorithm and the physical feasibility of the system.

Dynamics analysis of fractional-order permanent magnet synchronous motor and its DSP implementation

2019 ◽  
Vol 33 (06) ◽  
pp. 1950031 ◽  
Author(s):  
Dong Peng ◽  
Ke Hui Sun ◽  
Abdulaziz. O. A. Alamodi
Keyword(s):  
Permanent Magnet ◽  
Fractional Order ◽  
Digital Signal Processor ◽  
Permanent Magnet Synchronous Motor ◽  
Adomian Decomposition Method ◽  
Digital Signal ◽  
Accurate Method ◽  
Synchronous Motor ◽  
Computationally Efficient ◽  
Adomian Decomposition

In this paper, dynamics of the fractional-order permanent magnet synchronous motor (FOPMSM) model is investigated. The numerical solution of the FOPMSM system is derived based on Adomian decomposition method (ADM) that is a computationally efficient and high accurate method, and its dynamical behaviors are observed by means of phase diagrams, bifurcation diagrams, Lyapunov exponent spectra (LEs), Poincaré section and chaos diagram based on spectral entropy (SE) complexity. Comparison with some reported studies, the simulation results show that it has more rich dynamical characteristics. The lowest order for the existence of chaos is 2.115 that demonstrated by 0–1 test, which is lower than that existing result (2.85). Finally, the FOPMSM system is implemented by digital signal processor (DSP), which verifies the correctness of the solution algorithm and the physical feasibility of this system. It indicates that the FOPMSM system has broad application prospect.

scholarly journals Dynamics of Fractional-Order Digital Manufacturing Supply Chain System and Its Control and Synchronization

2021 ◽  
Vol 5 (3) ◽  
pp. 128
Author(s):  
Yingjin He ◽  
Song Zheng ◽  
Liguo Yuan
Keyword(s):  
Supply Chain ◽  
Fractional Order ◽  
Adomian Decomposition Method ◽  
Digital Manufacturing ◽  
Maximum Lyapunov Exponent ◽  
Supply Chain System ◽  
Chain System ◽  
Manufacturing Supply Chain ◽  
Adomian Decomposition ◽  
Control And Synchronization

Digital manufacturing is widely used in the production of automobiles and aircrafts, and plays a profound role in the whole supply chain. Due to the long memory property of demand, production, and stocks, a fractional-order digital manufacturing supply chain system can describe their dynamics more precisely. In addition, their control and synchronization may have potential applications in the management of real-word supply chain systems to control uncertainties that occur within it. In this paper, a fractional-order digital manufacturing supply chain system is proposed and solved by the Adomian decomposition method (ADM). Dynamical characteristics of this system are studied by using a phase portrait, bifurcation diagram, and a maximum Lyapunov exponent diagram. The complexity of the system is also investigated by means of SE complexity and C0 complexity. It is shown that the complexity results are consistent with the bifurcation diagrams, indicating that the complexity can reflect the dynamical properties of the system. Meanwhile, the importance of the fractional-order derivative in the modeling of the system is shown. Moreover, to further investigate the dynamics of the fractional-order supply chain system, we design the feedback controllers to control the chaotic supply chain system and synchronize two supply chain systems, respectively. Numerical simulations illustrate the effectiveness and applicability of the proposed methods.

Characteristic Analysis and DSP Realization of Fractional-Order Simplified Lorenz System Based on Adomian Decomposition Method

2015 ◽  
Vol 25 (06) ◽  
pp. 1550085 ◽  
Author(s):  
Huihai Wang ◽  
Kehui Sun ◽  
Shaobo He
Keyword(s):  
Fractional Order ◽  
Decomposition Method ◽  
Lorenz System ◽  
Adomian Decomposition Method ◽  
Qr Factorization ◽  
Iteration Step ◽  
Phase Portraits ◽  
Characteristic Analysis ◽  
Adomian Decomposition ◽  
Simplified Lorenz System

By adopting Adomian decomposition method, the fractional-order simplified Lorenz system is solved and implemented on a digital signal processor (DSP). The Lyapunov exponent (LE) spectra of the system is calculated based on QR-factorization, and it accords well with the corresponding bifurcation diagrams. We analyze the influence of the parameter and the fractional derivative order on the system characteristics by color maximum LE (LEmax) and chaos diagrams. It is found that the smaller the order is, the larger the LEmax is. The iteration step size also affects the lowest order at which the chaos exists. Further, we implement the fractional-order simplified Lorenz system on a DSP platform. The phase portraits generated on DSP are consistent with the results that were obtained by computer simulations. It lays a good foundation for applications of the fractional-order chaotic systems.

scholarly journals Dynamics and Complexity Analysis of Fractional-Order Chaotic Systems with Line Equilibrium Based on Adomian Decomposition

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Heng Chen ◽  
Tengfei Lei ◽  
Su Lu ◽  
WenPeng Dai ◽  
Lijun Qiu ◽  
...  
Keyword(s):  
Lyapunov Exponent ◽  
Fractional Order ◽  
Complexity Analysis ◽  
Adomian Decomposition Method ◽  
Order System ◽  
Largest Lyapunov Exponent ◽  
Initial Value ◽  
Adomian Decomposition ◽  
Line Equilibrium ◽  
Lyapunov Exponent Spectrum

In this paper, the Adomian decomposition method (ADM) is applied to solve the fractional-order system with line equilibrium. The dynamics of the system is analyzed by means of the Lyapunov exponent spectrum, bifurcations, chaotic attractor, and largest Lyapunov exponent diagram. At the same time, through the Lyapunov exponent spectrum and bifurcation graph of the system under the change of the initial value, the influence of fractional order q on the system state can be observed. That is, integer-order systems do not have the phenomenon of attractors coexistence, while fractional-order systems have it.

Implementation of fractional optimal control problems in real-world applications

2020 ◽  
Vol 23 (6) ◽  
pp. 1783-1796
Author(s):  
Neelam Singha
Keyword(s):  
Optimal Control ◽  
Fractional Order ◽  
Adomian Decomposition Method ◽  
Necessary Optimality Conditions ◽  
Order Model ◽  
Fractional Optimal Control ◽  
Adomian Decomposition ◽  
Real World Applications ◽  
Fractional Optimal Control Problems ◽  
And Control

Abstract In this article, we aim to analyze a mathematical model of tumor growth as a problem of fractional optimal control. The considered fractional-order model describes the interaction of effector-immune cells and tumor cells, including combined chemo-immunotherapy. We deduce the necessary optimality conditions together with implementing the Adomian decomposition method on the suggested fractional-order optimal control problem. The key motive is to perform numerical simulations that shall facilitate us in understanding the behavior of state and control variables. Further, the graphical interpretation of solutions effectively validates the applicability of the present analysis to investigate the growth of cancer cells in the presence of medical treatment.

scholarly journals An Efficient Analytical Technique, for The Solution of Fractional-Order Telegraph Equations

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 426 ◽  
Author(s):  
Hassan Khan ◽  
Rasool Shah ◽  
Poom Kumam ◽  
Dumitru Baleanu ◽  
Muhammad Arif
Keyword(s):  
Fractional Order ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Analytical Techniques ◽  
Telegraph Equation ◽  
High Rate ◽  
Analytical Technique ◽  
Decomposition Procedure ◽  
Adomian Decomposition ◽  
Telegraph Equations

In the present article, fractional-order telegraph equations are solved by using the Laplace-Adomian decomposition method. The Caputo operator is used to define the fractional derivative. Series form solutions are obtained for fractional-order telegraph equations by using the proposed method. Some numerical examples are presented to understand the procedure of the Laplace-Adomian decomposition method. As the Laplace-Adomian decomposition procedure has shown the least volume of calculations and high rate of convergence compared to other analytical techniques, the Laplace-Adomian decomposition method is considered to be one of the best analytical techniques for solving fractional-order, non-linear partial differential equations—particularly the fractional-order telegraph equation.

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