In this paper, we study the number of limit cycles of a near-Hamiltonian system having Za- equivariant quintic perturbations. Using the methods of Hopf and heteroclinic bifurcation theory, we find that the perturbed s...In this paper, we study the number of limit cycles of a near-Hamiltonian system having Za- equivariant quintic perturbations. Using the methods of Hopf and heteroclinic bifurcation theory, we find that the perturbed system can have 28 limit cycles, and its location is also given. The main result can be used to improve the lower bound of the maximal number of limit cycles for some polynomial systems in a previous work, which is the main motivation of the present paper.展开更多
This paper studies the number of limit cycles of some Z3-equivariant near-Hamiltonian systems of degrees 3 and 4,which are a perturbation of a cubic Hamiltonian system. By the Melnikov function method,we obtain 5 and ...This paper studies the number of limit cycles of some Z3-equivariant near-Hamiltonian systems of degrees 3 and 4,which are a perturbation of a cubic Hamiltonian system. By the Melnikov function method,we obtain 5 and 6 limit cycles respectively.展开更多
We study the limit cycle bifurcations perturbing a class of quartic linear-like Hamiltonian systems having an elementary center at the origin. First, using methods of the qualitative theory, all possible phase portrai...We study the limit cycle bifurcations perturbing a class of quartic linear-like Hamiltonian systems having an elementary center at the origin. First, using methods of the qualitative theory, all possible phase portraits of the unperturbed system are found. Then, using the first order Melnikov function, Hopf bifurcation problem of the perturbed system is investigated, and an upper bound for the function is obtained near the origin.展开更多
In this paper we deal with a cubic near-Hamiltonian system whose unperturbed system is a simple cubic Hamiltonian system having a nilpotent center. We prove that the system can have 5 limit cycles by using bifurcation...In this paper we deal with a cubic near-Hamiltonian system whose unperturbed system is a simple cubic Hamiltonian system having a nilpotent center. We prove that the system can have 5 limit cycles by using bifurcation theory.展开更多
In the study of the number of limit cycles of near-Hamiltonian systems,the first order Melnikov function plays an important role.This paper aims to generalize Horozov-Iliev’s method to estimate the upper bound of the...In the study of the number of limit cycles of near-Hamiltonian systems,the first order Melnikov function plays an important role.This paper aims to generalize Horozov-Iliev’s method to estimate the upper bound of the number of zeros of the function.展开更多
In this paper, we are concerned with a cubic near-Hamiltonian system, whose unperturbed system is quadratic and has a symmetric homoclinic loop. By using the method developed in [12], we find that the system can have ...In this paper, we are concerned with a cubic near-Hamiltonian system, whose unperturbed system is quadratic and has a symmetric homoclinic loop. By using the method developed in [12], we find that the system can have 4 limit cycles with 3 of them being near the homoclinic loop. Further, we give a condition under which there exist 4 limit cycles.展开更多
基金Supported by National Natural Science Foundation of China(Grant Nos.11271261,11461001)
文摘In this paper, we study the number of limit cycles of a near-Hamiltonian system having Za- equivariant quintic perturbations. Using the methods of Hopf and heteroclinic bifurcation theory, we find that the perturbed system can have 28 limit cycles, and its location is also given. The main result can be used to improve the lower bound of the maximal number of limit cycles for some polynomial systems in a previous work, which is the main motivation of the present paper.
基金supported by Leading Academic Discipline Project of Shanghai Normal University (DZL707)the National Ministry of Education of China (20060270001)Shanghai Leading Academic Discipline Project (S30405)
文摘This paper studies the number of limit cycles of some Z3-equivariant near-Hamiltonian systems of degrees 3 and 4,which are a perturbation of a cubic Hamiltonian system. By the Melnikov function method,we obtain 5 and 6 limit cycles respectively.
基金supported by the National Natural Science Foundations of China(12371171)and the Natural Science Foundation of Jiangsu Province(BK20221339).
文摘We study the limit cycle bifurcations perturbing a class of quartic linear-like Hamiltonian systems having an elementary center at the origin. First, using methods of the qualitative theory, all possible phase portraits of the unperturbed system are found. Then, using the first order Melnikov function, Hopf bifurcation problem of the perturbed system is investigated, and an upper bound for the function is obtained near the origin.
文摘In this paper we deal with a cubic near-Hamiltonian system whose unperturbed system is a simple cubic Hamiltonian system having a nilpotent center. We prove that the system can have 5 limit cycles by using bifurcation theory.
基金the Natural Science Foundation of Anhui Province(1308085MA08)the Doctor Program Foundation(2012)of Anhui Normal University+1 种基金the NNSF of China(11271197)the key NSF of Education Ministry of China(207047)
基金supported by National Natural Science Foundation of China(Grant Nos.11931016 and 11771296)Hunan Provincial Education Department(Grant No.19C1898).
文摘In the study of the number of limit cycles of near-Hamiltonian systems,the first order Melnikov function plays an important role.This paper aims to generalize Horozov-Iliev’s method to estimate the upper bound of the number of zeros of the function.
基金the National Natural Science Foundation of China under Grant (No.10671127)by Shanghai Shuguang Genzong Project(04SGG05)
文摘In this paper, we are concerned with a cubic near-Hamiltonian system, whose unperturbed system is quadratic and has a symmetric homoclinic loop. By using the method developed in [12], we find that the system can have 4 limit cycles with 3 of them being near the homoclinic loop. Further, we give a condition under which there exist 4 limit cycles.
