Usually, we reduce the problem on the Poincare Bifurcation to study thenumber and multiplicity of the zero roots for certain Abelian integrals. In thispaper, we use the method of [2] to study such problem from a diffe...Usually, we reduce the problem on the Poincare Bifurcation to study thenumber and multiplicity of the zero roots for certain Abelian integrals. In thispaper, we use the method of [2] to study such problem from a different angle ofHopf bifurcation and try to make clear all the possible Poincare Bifurcations ofsystem (1).展开更多
In this paper, we discuss the Poincaré bifurcation of a class of Hamiltonian systems having a region consisting of periodic cycles bounded by a parabola and a straight line. We prove that the system can generate ...In this paper, we discuss the Poincaré bifurcation of a class of Hamiltonian systems having a region consisting of periodic cycles bounded by a parabola and a straight line. We prove that the system can generate at most two limit cycles and may generate two limit cycles after a small cubic polynomial perturbation.展开更多
A class of polynomial system was structured, which depends on a parameter delta. When delta monotonous changes, more than one neighbouring limit cycles located in the vector field of this polynomial system can expand ...A class of polynomial system was structured, which depends on a parameter delta. When delta monotonous changes, more than one neighbouring limit cycles located in the vector field of this polynomial system can expand (or reduce) together with thee. But the expansion (or reduction) of these limit cycles is not surely monotonous. This vector field is like the rotated vector field. So these limit cycles of the polynomial system are called to constitute an 'analogue rotated vector field' with delta. They may become an effective tool to study the bifurcation of multiple limit cycle or fine separatrix cycle.展开更多
In this paper, we discuss the Poincare bifurcation for a class of quadratic systems having a region consisting of periodic cycles bounded by a hyperbola and an arc of equator. We prove that the system can at most gene...In this paper, we discuss the Poincare bifurcation for a class of quadratic systems having a region consisting of periodic cycles bounded by a hyperbola and an arc of equator. We prove that the system can at most generate two limit cycles after a small perturbation.展开更多
In this paper, we discuss the Poincare bifurcation of a cubic Hamiltonian system with homoclinic loop. We prove that the system can generate at most seven limit cycles after a small perturbation of general cubic polyn...In this paper, we discuss the Poincare bifurcation of a cubic Hamiltonian system with homoclinic loop. We prove that the system can generate at most seven limit cycles after a small perturbation of general cubic polynomials.展开更多
In this paper, we discuss the Poincaré bifurcation for a class of quadratic systems with an unbounded triangular region and a center region. It is proved, by Poincaré bifurcation, that inside the center regi...In this paper, we discuss the Poincaré bifurcation for a class of quadratic systems with an unbounded triangular region and a center region. It is proved, by Poincaré bifurcation, that inside the center region quadratic system perturbed by quadratic polynomial perturbation may generate three limit cycles.展开更多
In this paper, we investigate the Poincar bifurcation in cubic Hamiltonian systems with heteroclinic loop, under small general cubic perturbations. We prove that the system has at most two limit cycles and has at leas...In this paper, we investigate the Poincar bifurcation in cubic Hamiltonian systems with heteroclinic loop, under small general cubic perturbations. We prove that the system has at most two limit cycles and has at least two limit cycles, respectively.展开更多
In this paper, we discuss the Poincaré bifurcation of cubic Hamiltonian systems with double centers and prove that the systems may at least generate two limit cycles and at most generate three limit cycles outsid...In this paper, we discuss the Poincaré bifurcation of cubic Hamiltonian systems with double centers and prove that the systems may at least generate two limit cycles and at most generate three limit cycles outside the lemniscate after a small cubic perturbation展开更多
In order to provide the basis for parameter selection of vocal diseases classification,a nonlinear dynamic modeling method is proposed.A biomechanical model of vocal cords with polyp or paralysis,which couples to glot...In order to provide the basis for parameter selection of vocal diseases classification,a nonlinear dynamic modeling method is proposed.A biomechanical model of vocal cords with polyp or paralysis,which couples to glottal airflow to produce laryngeal sound source,is introduced.And then the fundamental frequency and its perturbation parameters are solved.Poincare section and bifurcation diagram are applied to nonlinear analysis of model vibration.By changing the pathological parameters or subglottal pressure,the changes of fundamental frequency and Lyapunov exponents are analyzed.The simulation results show that,vocal cord paralysis reduces the fundamental frequency,and the chaos occurs only within a certain pressure range;while vocal cord with a polyp don＇t reduce the fundamental frequency,chaos distributes throughout the entire range of pressure.Therefore this study is helpful for classification of polyp and paralysis by the acoustic diagnoses.展开更多
文摘Usually, we reduce the problem on the Poincare Bifurcation to study thenumber and multiplicity of the zero roots for certain Abelian integrals. In thispaper, we use the method of [2] to study such problem from a different angle ofHopf bifurcation and try to make clear all the possible Poincare Bifurcations ofsystem (1).
文摘In this paper, we discuss the Poincaré bifurcation of a class of Hamiltonian systems having a region consisting of periodic cycles bounded by a parabola and a straight line. We prove that the system can generate at most two limit cycles and may generate two limit cycles after a small cubic polynomial perturbation.
文摘A class of polynomial system was structured, which depends on a parameter delta. When delta monotonous changes, more than one neighbouring limit cycles located in the vector field of this polynomial system can expand (or reduce) together with thee. But the expansion (or reduction) of these limit cycles is not surely monotonous. This vector field is like the rotated vector field. So these limit cycles of the polynomial system are called to constitute an 'analogue rotated vector field' with delta. They may become an effective tool to study the bifurcation of multiple limit cycle or fine separatrix cycle.
文摘In this paper, we discuss the Poincare bifurcation for a class of quadratic systems having a region consisting of periodic cycles bounded by a hyperbola and an arc of equator. We prove that the system can at most generate two limit cycles after a small perturbation.
文摘In this paper, we discuss the Poincare bifurcation of a cubic Hamiltonian system with homoclinic loop. We prove that the system can generate at most seven limit cycles after a small perturbation of general cubic polynomials.
基金Supported by NSF and RFDP of China and China Postdoctoral Science Foundation (No.10471014).
文摘In this paper, we discuss the Poincaré bifurcation for a class of quadratic systems with an unbounded triangular region and a center region. It is proved, by Poincaré bifurcation, that inside the center region quadratic system perturbed by quadratic polynomial perturbation may generate three limit cycles.
文摘In this paper, we investigate the Poincar bifurcation in cubic Hamiltonian systems with heteroclinic loop, under small general cubic perturbations. We prove that the system has at most two limit cycles and has at least two limit cycles, respectively.
文摘In this paper, we discuss the Poincaré bifurcation of cubic Hamiltonian systems with double centers and prove that the systems may at least generate two limit cycles and at most generate three limit cycles outside the lemniscate after a small cubic perturbation
基金supported by the National Natural Science Foundation of China(61271359,61071215)the Biomedical Lab.of Jiemei in Soochow University
文摘In order to provide the basis for parameter selection of vocal diseases classification,a nonlinear dynamic modeling method is proposed.A biomechanical model of vocal cords with polyp or paralysis,which couples to glottal airflow to produce laryngeal sound source,is introduced.And then the fundamental frequency and its perturbation parameters are solved.Poincare section and bifurcation diagram are applied to nonlinear analysis of model vibration.By changing the pathological parameters or subglottal pressure,the changes of fundamental frequency and Lyapunov exponents are analyzed.The simulation results show that,vocal cord paralysis reduces the fundamental frequency,and the chaos occurs only within a certain pressure range;while vocal cord with a polyp don＇t reduce the fundamental frequency,chaos distributes throughout the entire range of pressure.Therefore this study is helpful for classification of polyp and paralysis by the acoustic diagnoses.
