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Analysis and implementation of new fractional-order multi-scroll hidden attractors

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Chinese Physics B 2021年第2期30卷 203-210页

作者：崔力雒文辉欧青立 Hunan University of Science and Technology Xiangtan 411201China

To improve the complexity of chaotic signals,in this paper we first put forward a new three-dimensional quadratic fractional-order multi-scroll hidden chaotic system,then we use the Adomian decomposition algorithm to solve the proposed fractional-order chaotic system and obtain the chaotic phase diagrams of different orders,as well as the Lyaponov exponent spectrum,bifurcation diagram,and SE complexity of the 0.99-order *** the process of analyzing the system,we find that the system possesses the dynamic behaviors of hidden attractors and hidden ***,we also propose a method of using the Lyapunov exponents to describe the basins of attraction of the chaotic system in the matlab environment for the first time,and obtain the basins of attraction under different order ***,we construct an analog circuit system of the fractional-order chaotic system by using an equivalent circuit module of the fractional-order integral operators,thus realizing the 0.9-order multi-scroll hidden chaotic attractors.

关键词： fractional order hidden attractor hidden bifurcation basins of attraction circuit implementation

On Computer Implementation for Comparison of Inverse Numerical Schemes for Non-Linear Equations

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Computer Systems Science & Engineering 2021年第3期36卷 493-507页

作者： Mudassir Shams Naila Rafiq Nazir Ahmad Mir Babar Ahmad Saqib Abbasi Mutee-Ur-Rehman Kayani Department of Mathematics and Statistics Riphah International UniversityI-14Islamabad44000Pakistan Department of Mathematics NUMLIslamabadPakistan Department of Mathematics Comsats UniversityIslamabad44000Pakistan

In this research article,we interrogate two new modifications in inverse Weierstrass iterative method for estimating all roots of non-linear equation *** modifications enables us to accelerate the convergence order of inverse Weierstrass method from 2 to *** analysis proves that the orders of convergence of the two newly constructed inverse methods are *** computer algebra system Mathematica,we find the lower bound of the convergence order and verify it *** planes of the inverse simultaneous methods and classical iterative methods are generated using MATLAB(R2011b),to present the global convergence properties of inverse simultaneous iterative methods as compared to classical *** non-linear models are taken from Physics,Chemistry and engineering to demonstrate the performance and efficiency of the newly constructed *** CPU time,and residual graphs of the methods are provided to present the dominance behavior of our newly constructed methods as compared to existing inverse and classical simultaneous iterative methods in the literature.

关键词： Non-linear equation inverse iterative method simultaneous method basins of attraction lower bound of convergence

Dynamical Comparison of Several Third-Order Iterative Methods for Nonlinear Equations

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Computers, Materials & Continua 2021年第5期67卷 1951-1962页

作者： Obadah Said Solaiman Samsul Ariffin Abdul Karim Ishak Hashim Department of Mathematical Sciences Faculty of Science&TechnologyUniversiti Kebangsaan MalaysiaBangi Selangor43600Malaysia Department of Fundamental and Applied Sciences Center for Smart Grid Energy Research(CSMER)Institute of Autonomous SystemUniversiti Teknologi PETRONASBandar Seri IskandarSeri IskandarPerak DR32610Malaysia

There are several ways that can be used to classify or compare iterative methods for nonlinear equations,for instance;order of convergence,informational efficiency,and efficiency *** this work,we use another way,namely the basins of attraction of the *** purpose of this study is to compare several iterative schemes for nonlinear *** the selected schemes are of the third-order of convergence and most of them have the same efficiency *** comparison depends on the basins of attraction of the iterative techniques when applied on several polynomials of different *** a comparison,we determine the CPU time(in seconds)needed by each scheme to obtain the basins of attraction,besides,we illustrate the area of convergence of these schemes by finding the number of convergent and divergent points in a selected range for all *** confirm the fact that basins of attraction differ for iterative methods of different orders,furthermore,they vary for iterative methods of the same order even if they have the same efficiency ***,this leads to the need for a new index that reflects the real efficiency of the iterative scheme instead of the commonly used efficiency index.

关键词： Nonlinear equations iterative methods basins of attraction order of convergence

Impact of radiation pressure and circumstellar dust on motion of a test particle in Manev’s field

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Astrodynamics 2021年第2期5卷 77-89页

作者： Jagadish Singh Solomon Okpanachi Omale Lawrence O.Inumoh Felix Ale Department of Mathematics Faculty of Physical SciencesAhmadu Bello UniversityZariaNigeria Engineering and Space Systems Department National Space Research and Development Agency(NASRDA)Obasanjo Space CentreAbujaNigeria

In this paper,we present a study on the impact of radiation pressure and circumstellar dust on the motion of a test particle in the framework of the restricted four-body problem under the Manev’s *** show that the distribution of equilibrium points on the plane of motion is slightly different from that of the classical Newtonian *** the aid of the Lyapunov characteristic exponents,we show that the system is sensitive to changes in initial conditions;hence,the orbit of the system is found to be chaotic in the phase space for the given initial ***,a numerical application of this model to a stellar system(Gliese 667C)is considered,which validates the dependence of the equilibrium points on the mass *** show that the non-collinear equilibrium points of this stellar system are distributed symmetrically about the x-axis,and five of them are linearly *** basins of attraction of the system show that the equilibrium points have irregular boundaries,and we use the energy integral and the Manev parameter to illustrate the zero-velocity curves showing the permissible region of motion of the test particle with respect to the Jacobi constant.

关键词： Manev potential circumstellar dust Lyapunov characteristic exponents(LCEs) stability chaos basins of attraction