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Generation of countless embedded trumpet-shaped chaotic attractors in two opposite directions from a new three-dimensional system with no equilibrium point 被引量:1
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作者 孙常春 《Chinese Physics B》 SCIE EI CAS CSCD 2014年第9期133-137,共5页
A new three-dimensional (3D) continuous autonomous system with one parameter and three quadratic terms is presented firstly in this paper. Countless embedded trumpet-shaped chaotic attractors in two opposite directi... A new three-dimensional (3D) continuous autonomous system with one parameter and three quadratic terms is presented firstly in this paper. Countless embedded trumpet-shaped chaotic attractors in two opposite directions are generated from the system as time goes on. The basic dynamical behaviors of the strange chaotic system are investigated. Another more complex 3D system with the same capability of generating countless embedded trumpet-shaped chaotic attractors is also put forward. 展开更多
关键词 three-dimensional system trumpet-shaped chaotic attractor equilibrium point
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Directional Analysis of the Chaotic Superlattice around the Equilibrium Point in the Phase Space
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作者 Yan-Fei Liu Dong-Dong Yang +1 位作者 Li-Xin Wang Qi Li 《Chinese Physics Letters》 SCIE CAS CSCD 2018年第4期82-85,共4页
The recently proposed method of our research group named as directional Lyapunov exponents(DLEs) is presented. Then, DLEs are used to analyze the eigenstructure of the output phase space around the equilibrium point... The recently proposed method of our research group named as directional Lyapunov exponents(DLEs) is presented. Then, DLEs are used to analyze the eigenstructure of the output phase space around the equilibrium points. Finally, the impacts of the superlattice parameter changes on the characteristics of the output chaotic signal are analyzed. The experimental results show that parameter changes of the superlattice will affect the eigenstructure around the equilibrium points in the output phase space, and DLEs are sensitive to these changes. 展开更多
关键词 DLE Directional Analysis of the Chaotic Superlattice around the equilibrium point in the Phase Space
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On the Artificial Equilibrium Points in a Generalized Restricted Problem of Three Bodies 被引量:1
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作者 Kumari Ranjana Vijay Kumar 《International Journal of Astronomy and Astrophysics》 2013年第4期508-516,共9页
The present article studies the stability conditions of central control artificial equilibrium generalized restricted problem of three bodies. It is generalized in the sense that here we have taken the larger primary ... The present article studies the stability conditions of central control artificial equilibrium generalized restricted problem of three bodies. It is generalized in the sense that here we have taken the larger primary body to be in shape of an oblate spheroid. The equilibrium points are sought by the application of the propellant for which it would just balance the gravitational forces. The launching flight of such a satellite is seen to be applicable for having arbitrary space stations for these different missions. Specialty of the result of the investigation lies in the fact that an arbitrary space station can be formed to attain any specified mission. 展开更多
关键词 THREE-BODY Problem Artificial equilibrium pointS Minimum THRUST
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Existence of Equilibrium Points in the R3BP with Variable Mass When the Smaller Primary is an Oblate Spheroid
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作者 M. R. Hassan Sweta Kumari Md. Aminul Hassan 《International Journal of Astronomy and Astrophysics》 2017年第2期45-61,共17页
The paper deals with the existence of equilibrium points in the restricted three-body problem when the smaller primary is an oblate spheroid and the infinitesimal body is of variable mass. Following the method of smal... The paper deals with the existence of equilibrium points in the restricted three-body problem when the smaller primary is an oblate spheroid and the infinitesimal body is of variable mass. Following the method of small parameters;the co-ordinates of collinear equilibrium points have been calculated, whereas the co-ordinates of triangular equilibrium points are established by classical method. On studying the surface of zero-velocity curves, it is found that the mass reduction factor has very minor effect on the location of the equilibrium points;whereas the oblateness parameter of the smaller primary has a significant role on the existence of equilibrium points. 展开更多
关键词 RESTRICTED THREE-BODY Problem Jean’s Law Space-Time Transformation OBLATENESS equilibrium pointS Surface of Zero-Velocity
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Existence of Multiple Equilibrium Points in Global Attractor for the Strongly Damped Wave Equations
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作者 孟凤娟 汪永海 刘存才 《Journal of Donghua University(English Edition)》 EI CAS 2017年第3期448-452,共5页
The aim of this paper is to study the long-term behavior of strongly damped wave equations with a Lyapunov function. Using the theory established by estimating the Z2 index of some sets and the idea of invariant sets ... The aim of this paper is to study the long-term behavior of strongly damped wave equations with a Lyapunov function. Using the theory established by estimating the Z2 index of some sets and the idea of invariant sets of semi-flow,the properties of the global attractor for strongly damped wave equation are discussed. The existence of multiple equilibrium points in global attractor for strongly damped wave equations with critical growth of nonlinearity is obtained. And under some additional condition, the infinite dimension of the attractor is proven. 展开更多
关键词 infinite invariant nonlinearity estimating assumption proven proof regularity stationary neighborhood
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Artificial Equilibrium Points in the Low-Thrust Restricted Three-Body Problem When Both the Primaries Are Oblate Spheroids
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作者 Amit Mittal Krishan Pal 《International Journal of Astronomy and Astrophysics》 2018年第4期406-424,共19页
This paper studies the existence and stability of the artificial equilibrium points (AEPs) in the low-thrust restricted three-body problem when both the primaries are oblate spheroids. The artificial equilibrium point... This paper studies the existence and stability of the artificial equilibrium points (AEPs) in the low-thrust restricted three-body problem when both the primaries are oblate spheroids. The artificial equilibrium points (AEPs) are generated by canceling the gravitational and centrifugal forces with continuous low-thrust at a non-equilibrium point. Some graphical investigations are shown for the effects of the relative parameters which characterized the locations of the AEPs. Also, the numerical values of AEPs have been calculated. The positions of these AEPs will depend not only also on magnitude and directions of low-thrust acceleration. The linear stability of the AEPs has been investigated. We have determined the stability regions in the xy, xz and yz-planes and studied the effect of oblateness parameters A1(0A1?and ?A2(0A2<1) on the motion of the spacecraft. We have found that the stability regions reduce around both the primaries for the increasing values of oblateness of the primaries. Finally, we have plotted the zero velocity curves to determine the possible regions of motion of the spacecraft. 展开更多
关键词 RESTRICTED THREE-BODY Problem Artificial equilibrium points LOW-THRUST Stability Oblate SPHEROID Zero Velocity Curves
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GLOBAL STABILITY OF ENDEMIC EQUILIBRIUM POINT OF BASIC VIRUS INFECTION MODEL WITH APPLICATION TO HBV INFECTION 被引量:4
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作者 Yu ZHENG Lequan MIN +2 位作者 Yu JI Yongmei SU Yang KUANG 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2010年第6期1221-1230,共10页
In this paper, the authors first show that if Ro ≤1, the infection free steady state is globally attractive by using approaches different from those given by Min, et a1.(2008). Then the authors prove that if Ro 〉 ... In this paper, the authors first show that if Ro ≤1, the infection free steady state is globally attractive by using approaches different from those given by Min, et a1.(2008). Then the authors prove that if Ro 〉 1, the endemic steady state is also globally attractive. Finally, based on a patient's clinical HBV DNA data of anti-HBV infection with drug lamivudine, the authors establish an ABVIM. The numerical simulations of the ABVIM axe good in agreement with the clinical data. 展开更多
关键词 Basic infection reproduction number clinical data simulation equilibrium point global stability HBV infection.
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Artificial equilibrium points and bi-impulsive maneuvers to observe 243 Ida 被引量:1
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作者 Allan Kardec de ALMEIDA Jr Geraldo Magela Couto OLIVEIRA Antonio Fernando Bertachini de Almeida PRADO 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2021年第1期410-423,共14页
In the restricted three-body problem,the traditional Lagrange points L1 and L2 are the only equilibrium points near the asteroid 243 Ida.The thrust generated by a solar sail over a spacecraft enables the existence of ... In the restricted three-body problem,the traditional Lagrange points L1 and L2 are the only equilibrium points near the asteroid 243 Ida.The thrust generated by a solar sail over a spacecraft enables the existence of new artificial equilibrium points,which depend on the position of the spacecraft with respect to the asteroid and the attitude of the solar sail.Such equilibrium points generate new spots to observe the body from above or below the plane of motion.Such points are very good observational locations due to their stationary condition.This work provides a preliminary analysis to observe Ida through the use of artificial equilibrium points as spots combined with transfer maneuvers between them.Such combination can be used to observe the asteroid from more different points of view in comparison to fixed ones.The analyses are made for a spacecraft equipped with a solar sail and capable of performing bi-impulsive maneuvers.The solar radiation pressure is used both to maintain the equilibrium condition and to reduce the costs of the transfers and/or to create transfers with longer duration.This is a new aspect of the present research,because it combines the continuous thrust with initial and final small impulses,which are feasible for most of the spacecraft,because the magnitudes of the impulses are very low.These combined maneuvers may reduce the transfer times of the maneuvers in most of the cases,compared with the maneuvers based only on continuous thrust.Several options involved in these transfers are shown,like to minimize the fuel spent(Dv)as a function of the transfer time or to extend the duration of the travel between the points.Extended transfer times can be useful when observations are required during the transfers. 展开更多
关键词 Artificial equilibrium points ASTRODYNAMICS Orbital transfers Solar radiation pressure Solar sail
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Nash Equilibrium of a Fixed-Sum Two-Player Game
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作者 Yoshihiro Tanaka 《American Journal of Computational Mathematics》 2024年第3期346-357,共12页
It is well established that Nash equilibrium exists within the framework of mixed strategies in strategic-form non-cooperative games. However, finding the Nash equilibrium generally belongs to the class of problems kn... It is well established that Nash equilibrium exists within the framework of mixed strategies in strategic-form non-cooperative games. However, finding the Nash equilibrium generally belongs to the class of problems known as PPAD (Polynomial Parity Argument on Directed graphs), for which no polynomial-time solution methods are known, even for two-player games. This paper demonstrates that in fixed-sum two-player games (including zero-sum games), the Nash equilibrium forms a convex set, and has a unique expected payoff. Furthermore, these equilibria are Pareto optimal. Additionally, it is shown that the Nash equilibrium of fixed-sum two-player games can theoretically be found in polynomial time using the principal-dual interior point method, a solution method of linear programming. 展开更多
关键词 Nash equilibrium Fixed-Sum Two-Player Game Principal-Dual Interior point Method
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Equilibrium points and orbits around asteroid with the full gravitational potential caused by the 3D irregular shape 被引量:2
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作者 Yu Jiang 《Astrodynamics》 2018年第4期361-373,共13页
We investigate the equilibrium points and orbits around asteroid 1333 Cevenola by considering the full gravitational potential caused by the 3D irregular shape.The gravitational potential and effective potential of as... We investigate the equilibrium points and orbits around asteroid 1333 Cevenola by considering the full gravitational potential caused by the 3D irregular shape.The gravitational potential and effective potential of asteroid 1333 Cevenola are calculated.The zero-velocity curves for a massless particle orbiting in the gravitational environment have been discussed.The linearized dynamic equation,the characteristic equation,and the conserved quantity of the equilibria for the large-size-ratio binary asteroid system have been derived.It is found that there are totally five equilibrium points close to 1333 Cevenola.The topological cases of the outside equilibrium points have a staggered distribution.The simulation of orbits in the full gravitational potential caused by the 3D irregular shape of 1333 Cevenola shows that the moonlet’s orbit is more likely to be stable if the orbit inclination is small. 展开更多
关键词 equilibrium points ORBITS polyhedral model ASTEROIDS 1333 Cevenola
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Regional Stability of Positive Switched Linear Systems with Multi-equilibrium Points 被引量:2
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作者 Zhi Liu Yu-Zhen Wang 《International Journal of Automation and computing》 EI CSCD 2017年第2期213-220,共8页
This paper studies the regional stability for positive switched linear systems with multi-equilibrium points (PSLS-MEP). First, a sufficient condition is presented for the regional stability of PSLS-MEP via a common... This paper studies the regional stability for positive switched linear systems with multi-equilibrium points (PSLS-MEP). First, a sufficient condition is presented for the regional stability of PSLS-MEP via a common linear Lyapunov function. Second, by establishing multiple Lyapunov functions, a dwell time based condition is proposed for the regional stability analysis. Third, a suprasphere which contains all equilibrium points is constructed as a stability region of the considered PSLS-MEP, which is less conservative than existing results. Finally, the study of an illustrative example shows that the obtained results are effective in the regional stability analysis of PSLS-MEP. 展开更多
关键词 Regional stability positive switched linear system multi-equilibrium points common linear Lyapunov function multipleLyapunov function.
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Non-equatorial equilibrium points around an asteroid with gravitational orbit-attitude coupling perturbation 被引量:1
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作者 Yue Wang Shijie Xu 《Astrodynamics》 CSCD 2020年第1期1-16,共16页
A recently proposed orbital dynamics model in the close proximity of an asteroid,which is called“attitude-restricted orbital dynamics”,includes the perturbation caused by the spacecraft’s gravitational orbit-attitu... A recently proposed orbital dynamics model in the close proximity of an asteroid,which is called“attitude-restricted orbital dynamics”,includes the perturbation caused by the spacecraft’s gravitational orbit-attitude coupling.This orbital model improves the precision of classical point-mass orbital model with only the non-spherical gravity.Equatorial equilibrium points have been investigated in the previous paper.In this paper,the inplane non-equatorial equilibrium points,which are outside the asteroid’s equatorial plane but within its longitudinal principal plane,are further studied for a uniformly-rotating asteroid.These non-equatorial equilibrium points are more diverse than those in the classical point-mass orbital dynamics without gravitational orbit-attitude coupling perturbation(GOACP).Two families of them have been found.The equatorial equilibrium points studied before and the non-equatorial ones studied here give a complete map of equilibrium points in the asteroid’s principal planes.Compared with the classical point-mass orbital dynamics without GOACP,the equatorial equilibrium points have extended the longitude range of equilibrium points around an asteroid,while the non-equatorial ones studied here will extend the latitude range.These equatorial and non-equatorial equilibrium points provide natural hovering positions for the asteroid close-proximity operations. 展开更多
关键词 asteroid mission gravitational orbit-attitude coupling perturbation(GOACP) attitude-restricted orbital dynamics non-equatorial equilibrium points
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Distribution of static equilibrium points in static electric field produced by fixed electrons
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作者 GUO Feng 《The Journal of China Universities of Posts and Telecommunications》 EI CSCD 2014年第4期92-95,共4页
Fix n electrons on the disk |z|≤R. They generate a static electric field. Let a be an electron located in the disk |z|≤R sin π/n. It shows that the closed disk with center a and radius R contains at least one s... Fix n electrons on the disk |z|≤R. They generate a static electric field. Let a be an electron located in the disk |z|≤R sin π/n. It shows that the closed disk with center a and radius R contains at least one static equilibrium point. 展开更多
关键词 fixed electrons static electric field static equilibrium points
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5D Hyper-Chaotic System with Multiple Types of Equilibrium Points
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作者 XU Changbiao WU Xia +1 位作者 HE Yinghui MO Yunhui 《Journal of Shanghai Jiaotong university(Science)》 EI 2020年第5期639-649,共11页
A chaotic system with various equilibrium types has rich dynamic behaviors.Its state can switch flexibly among different families of attractors,which is beneficial to the practical applications.So it has been widely c... A chaotic system with various equilibrium types has rich dynamic behaviors.Its state can switch flexibly among different families of attractors,which is beneficial to the practical applications.So it has been widely concerned in recent years.In this paper,a new 5D hyper-chaotic system is proposed.The important characteristic of the system is that it may have multiple types of equilibrium points by changing system parameters,namely,linear equilibrium point,no equilibrium point,non-hyperbolic unstable equilibrium point and stable hyperbolictype equilibrium point.Furthermore,there are hyper-chaotic phenomena and multi-stability about the coexistence of multiple chaotic attractors and the coexistence of hyper-chaotic attractors and chaotic attractors in the system.In addition,the system,complexity is analyzed.It is found that the complexity is close to 1 in the hyper-chaotic state and a pseudo-random sequence generated by the system passes all the statistical tests.Finally,an analog circuit of the system is designed and simulated. 展开更多
关键词 HYPER-CHAOS equilibrium point multi-stability pseudorandom sequence chaotic circuit
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Out-of-plane equilibrium points and invariant manifolds about an asteroid with gravitational orbit–attitude coupling perturbation
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作者 Yue Wang Ruikang Zhang 《Astrodynamics》 EI CSCD 2022年第3期269-283,共15页
By considering the spacecraft as an extended,rigid body with a prior known attitude instead of a point mass,the attitude-restricted orbital dynamics can improve the precision of the classical point-mass orbital dynami... By considering the spacecraft as an extended,rigid body with a prior known attitude instead of a point mass,the attitude-restricted orbital dynamics can improve the precision of the classical point-mass orbital dynamics in close proximity to an asteroid,because it includes the perturbation caused by the gravitational orbit–attitude coupling of the spacecraft(GOACP).The GOACP is defined as the difference between the gravity acting on a non-spherical,extended body(the real case of a spacecraft)and the gravity acting on a point mass(the approximation of a spacecraft in classical orbital dynamics).Inplane equilibrium points that are within the principal planes of the asteroid have been investigated for the attitude-restricted orbital dynamics in previous studies,including equatorial and in-plane non-equatorial equilibrium points.In this study,out-of-plane equilibrium points outside the principal planes of the asteroid were examined.Out-ofplane equilibrium points cannot exist in the classical point-mass orbital dynamics but do exist in the attitude-restricted orbital dynamics owing to the effects of the GOACP.The previously investigated in-plane equilibrium points and the out-of-plane ones examined in this study provide a complete map of the equilibrium points in close proximity to an asteroid with the GOACP.Equatorial and in-plane non-equatorial equilibrium points have extended the longitude and latitude ranges of the classical equilibrium points without the GOACP,respectively,while the out-of-plane ones examined in the present study extend both the longitude and latitude ranges.Additionally,the invariant manifolds of out-of-plane equilibrium points were calculated,and the results indicated that the attitude of spacecraft significantly affects the invariant manifolds.In practice,these equilibrium points can provide natural hovering positions for operations in proximity to asteroids,and their invariant manifolds can be used for transfers to or from the equilibrium points. 展开更多
关键词 asteroid mission attitude-restricted orbital dynamics gravitational orbit-attitude coupling perturbation(GOACP) out-of-plane equilibrium points invariant manifolds
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New method for computing unstable equilibrium points of power systems with induction motors 被引量:3
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作者 CHEN Lei,XU Fei & MIN Yong State Key Lab of Power Systems,Department of Electrical Engineering,Tsinghua University,Beijing 100084,China 《Science China(Technological Sciences)》 SCIE EI CAS 2010年第4期881-885,共5页
The computation of the unstable equilibrium point(UEP) is a key step involved in stability region estimation of nonlinear dynamic systems.A new continuation-based method to compute the UEPs of a power system with indu... The computation of the unstable equilibrium point(UEP) is a key step involved in stability region estimation of nonlinear dynamic systems.A new continuation-based method to compute the UEPs of a power system with induction motors is proposed.The mechanical torques of motors are changed to form a parameterized equation set.Then the solution curve of the equation set is traced by the continuation method from the stable equilibrium point to a UEP.The direction of mechanical torque change is varied to get multiple UEPs.The obtained UEPs are mostly type-1.Then fast assessment of induction motor stability is studied by approximating the stable manifolds of the UEPs.The method is tested in several systems and satisfactory results are obtained. 展开更多
关键词 power system STABILITY transient voltage STABILITY UNSTABLE equilibrium point(UEP) STABILITY boundary induction motor
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Quadratic minimization for equilibrium problem variational inclusion and fixed point problem
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作者 张石生 李向荣 陈志坚 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2010年第7期917-928,共12页
The purpose of this paper is to find the solutions to the quadratic mini- mization problem by using the resolvent approach. Under suitable conditions, some new strong convergence theorems are proved for approximating ... The purpose of this paper is to find the solutions to the quadratic mini- mization problem by using the resolvent approach. Under suitable conditions, some new strong convergence theorems are proved for approximating a solution of the above min- imization problem. The results presented in the paper extend and improve some recent results. 展开更多
关键词 quadratic minimization generalized equilibrium fixed point variational inclusion multi-valued maximal monotone mapping inverse-strongly monotone mapping resolvent operator nonexpansive mapping
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Strong Convergence of an Iterative Method for Generalized Mixed Equilibrium Problems and Fixed Point Problems 被引量:1
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作者 Lijun Chen Jianhua Huang 《Applied Mathematics》 2011年第10期1213-1220,共8页
In this paper, we introduce a hybrid iterative method for finding a common element of the set of common solutions of generalized mixed equilibrium problems and the set of common fixed points of an finite family of non... In this paper, we introduce a hybrid iterative method for finding a common element of the set of common solutions of generalized mixed equilibrium problems and the set of common fixed points of an finite family of nonexpansive mappings. Furthermore, we show a strong convergence theorem under some mild conditions. 展开更多
关键词 Generalized Mixed equilibrium Problem Hybrid ITERATIVE Scheme Fixed point NONEXPANSIVE Mapping STRONG Convergence
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Algorithms for Common Solutions to Generalized Mixed Equilibrium Problems and Fixed Point Problems under Nonlinear Transformations in Banach Spaces 被引量:1
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作者 Yanlai Song Xinhong Chen 《Journal of Applied Mathematics and Physics》 2019年第11期2632-2649,共18页
The purpose of this paper is to present a new iterative scheme for finding a common solution of the generalized mixed equilibrium problems with an infinite family of inverse strongly monotone mappings and the fixed po... The purpose of this paper is to present a new iterative scheme for finding a common solution of the generalized mixed equilibrium problems with an infinite family of inverse strongly monotone mappings and the fixed point problems of demimetric mappings under nonlinear transformations in Banach spaces. Applications are also included. The results in this paper are the extension and improvement of the recent results in the literature. 展开更多
关键词 Fixed point Demimetric Mapping GENERALIZED MIXED equilibrium Problems BANACH Space
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Convergence Theorem of Hybrid Iterative Algorithm for Equilibrium Problems and Fixed Point Problems of Finite Families of Uniformly Asymptotically Nonexpansive Semigroups
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作者 Hongbo Liu Yi Li 《Advances in Pure Mathematics》 2014年第6期244-252,共9页
Throughout this paper, we introduce a new hybrid iterative algorithm for finding a common element of the set of common fixed points of a finite family of uniformly asymptotically nonexpansive semigroups and the set of... Throughout this paper, we introduce a new hybrid iterative algorithm for finding a common element of the set of common fixed points of a finite family of uniformly asymptotically nonexpansive semigroups and the set of solutions of an equilibrium problem in the framework of Hilbert spaces. We then prove the strong convergence theorem with respect to the proposed iterative algorithm. Our results in this paper extend and improve some recent known results. 展开更多
关键词 HYBRID Iterative Algorithm UNIFORMLY ASYMPTOTICALLY NONEXPANSIVE SEMIGROUPS equilibrium Problem Common Fixed point
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