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ON　 THE　 NONEXISTENCE　 OF 　THE 　limit　 cycleFOR　 QUADRATIC　 SYSTEM　 OF　 TYPE III

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Annals of Differential Equations 1999年第1期15卷 77-82页

作者：徐思林

In tills paper, several new criteria on the nonexistence of limit cycles forquadratic system of Type III are given.

关键词： qlladratic system of Type III limit cycle nonexistenceAMS Subject Classification 34C05

ON A CONJECTURE CONCERNING THE NON-EXISTENCE OF limit cycleS FOR QUADRATIC DIFFERENTIAL SYSTEMS

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Annals of Differential Equations 2000年第4期16卷 391-400页

作者：叶彦谦

A conjecture on the non-existence of limit cycles for the quadratic differential system (1) under conditions (2) and iv) of (3) is discussed; interesting phenomena are revealed.

关键词： limit cycle quadratic differential system divergence

ANALYSIS OF limit cycleS TO A PERTURBED INTEGRABLE NON-HAMILTONIAN SYSTEM

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Annals of Differential Equations 2012年第3期28卷 263-268页

作者： Xiaochun Hong1,2,Yunqiu Wang1,Xuemei Zhang2 1.School of Statistics and Math.,Yunnan University of Finance and Economics,Kunming 650221 2.School of Math.and Information Science,Qujing Normal University,Qujing 655011,Yunnan

Bifurcation of limit cycles to a perturbed integrable non-Hamiltonian system is investigated using both qualitative analysis and numerical *** investigation is based on detection functions which are particularly effective for the perturbed integrable non-Hamiltonian *** study reveals that the system has 3 limit *** the method of numerical simulation,the distributed orderliness of the 3 limitcycles is observed,and their nicety places are *** study also indicates that each of the 3 limit cycles passes the corresponding nicety point.

关键词： limit cycle integrable non-Hamiltonian system detection function numerical exploration

THE limit cycleS AND HOPF BIFURCATION OF A CLASS OF SIMPLIFIED HOLLING TYPE-IV PREDATOR-PREY SYSTEM WITH LINEAR STATE FEEDBACK

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Annals of Differential Equations 2010年第1期26卷 53-58页

作者： Zhigao Shi Jinshan College, Fujian Agriculture and Forestry University, Fuzhou 350002

In this paper, a class of simplified Type-IV predator-prey system with linear state feedback is investigated. We prove the boundedness of the positive solutions to this system, and analyze the quality of the equilibria and the existence of limit cycles of the system surrounding the positive equilibra. By Hopf bifurcation theory, the result of having two limit cycles to the system is obtained.

关键词： linear state feedback Holling-IV boundedness limit cycle Hopf bifurcation

ON THE NUMBER OF limit cycleS OF A CUBIC SYSTEM NEAR A CUSPIDAL LOOP

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Annals of Differential Equations 2010年第2期26卷 222-226页

作者： Yun Tian, Yepeng Xing (Dept. of Math., Shanghai Normal University, Shanghai 200234)

In this paper, we investigate the limit cycle bifurcations in a cubic near-Hamiltonian system by perturbing a cuspidal loop and prove that 5 limit cycles can appear in a neighborhood of the cuspidal loop.

关键词： cuspidal loop Melnikov function limit cycle bifurcation

Singular Homoclinic Orbits and limit cycles in Positive Second Order Slow-Fast Systems

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Journal of Mathematical Research and Exposition 2004年第1期24卷 49-54页

作者：肖箭盛立人安徽大学数学系安徽合肥230039

In the paper we consider a wide class of slow-fast second order systems and give sufficient conditions for the existence of a singular limit cycle related to a homoclinic orbit.

关键词： homoclinic orbit limit cycle singular perturbation slow manifold.

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一类多项式系统极限环存在的充要条件

Northeastern Mathematical Journal 2004年第1期20卷 13-22页

作者：薛春艳姚波刘德明 DepartmentofAppliedMathematics BeijingInstituteofTechnologyBeijing100081 DepartmentofMathematics ShenyangNormalUniversityShenyang110034

In this paper, the following polynomial system is discussed: dx/dt=y[1+B(x)],dy/dt=(-x^α+δy+α1x^2α+α2x^αy+a5x^2αy)A(1+C(x)].And the necessary and sufficient conditions of existence and uniqueness of limit cycle... 详细信息

关键词： polynorial system limit cycle existence and uniqueness

EXISTENCE AND UNIQUENESS OF limit cycleS FOR A CLASS OF CUBIC DIFFERENTIAL SYSTEM

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Annals of Differential Equations 2013年第4期29卷 490-492页

作者： Weide Zhang Hunan College of Information

In this paper we consider the existence, uniqueness and nonexistence of limit cycles for the class of planar cubic system x=-y+δx+a2xy+a3x2+a7x3, y=x, where a7≠0.

关键词： uniqueness limit cycle existence cubic

The Topology of the Sectional Streamlines

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Communications in Nonlinear Science and Numerical Simulation 1998年第4期3卷 203-206页

作者： Lixin GE and Qingdong CAI(Lab. Of Comp. Phys., IAPCM, P.O.Box 8009, Beijing 100088,China) Lab. of Comp. Phys. IAPCM P.O.Box 8009 Beijing 100088 China

The unsteadyl three-dimensional full Navier-Stokes equations are solved using a Beam-Warming implicit algorithm in this paper. Computations of the flow over a 76°sweep delta wing at 36.5° angle of attack is presented. The sectional streamlines are depicted and the evolution of the instantaneous crossflow topology of the leading-edge vortex is analyzed. It is found that, along the axis, the topology of the primary vortex alters several times starting from stable focus near the apex to unstable focus, and lasts back to stable focus near wake edge; The stable limit cycle and unstable lint cycle are shown in this evolution. These various altering topologies stem from the stretching and compression of the vortex core.

关键词： : sectional streamline limit cycle focus