An upper bound B(n)≤ 12{7n+12((-1) n-1)} is derived for the number of zeros of Abelian integralsI(h)=∮ Γ h g(x,y)dy-f(x,y)dx on the open interval (-112,0)∪ (0,+∞), where Γ h is the...An upper bound B(n)≤ 12{7n+12((-1) n-1)} is derived for the number of zeros of Abelian integralsI(h)=∮ Γ h g(x,y)dy-f(x,y)dx on the open interval (-112,0)∪ (0,+∞), where Γ h is the compact component of the algebraic curve H(x,y)=12y 2+13x 3+14x 4=h,f(x,y) and g(x,y) are polynomials of x and y,n= max s{ deg f(x,y), deg g(x,y)} .展开更多
In this paper, we study the periodic wave propagation phenomenon in elastic waveguides modeled by a combined double-dispersive partial differential equation(PDE).The traveling wave ansazt transforms the PDE model into...In this paper, we study the periodic wave propagation phenomenon in elastic waveguides modeled by a combined double-dispersive partial differential equation(PDE).The traveling wave ansazt transforms the PDE model into a perturbed integrable ordinary differential equation(ODE). The global bifurcation theory is applied for the perturbed ODE model to establish the existence and uniqueness of the limit cycle, which corresponds the periodic traveling wave for the PDE model. The main tool is the Abelian integral taken from Poincaré bifurcation theory. Simulation is carried out to verify the theoretical result.展开更多
In this paper, the KP-MEW(2,2) equation is considered under a certain parametric condition. We prove that the equation has two isochronous centers under certain parametric conditions, and there exist two families of p...In this paper, the KP-MEW(2,2) equation is considered under a certain parametric condition. We prove that the equation has two isochronous centers under certain parametric conditions, and there exist two families of periodic solutions with equal period.展开更多
Abstract This paper is devoted to the study of the period function for a class of reversible quadratic system x=-2xy,y=k-1-2kx＋（k＋1）x^2-1/2y^2.We determine the monotonicity of the period function for each k ∈ R....Abstract This paper is devoted to the study of the period function for a class of reversible quadratic system x=-2xy,y=k-1-2kx＋（k＋1）x^2-1/2y^2.We determine the monotonicity of the period function for each k ∈ R. It is proved that the period function has at most one critical point.展开更多
In this paper,we consider Li′enard systems of the form dx/dt=y,dy/dt=x＋bx3-x5＋ε（α＋βx2＋γx4）y,where b∈R,0〈｜ε｜〈〈1,（α,β,γ）∈D∈R3 and D is bounded.We prove that for ｜b｜〉〉1（b〈0） the least uppe...In this paper,we consider Li′enard systems of the form dx/dt=y,dy/dt=x＋bx3-x5＋ε（α＋βx2＋γx4）y,where b∈R,0〈｜ε｜〈〈1,（α,β,γ）∈D∈R3 and D is bounded.We prove that for ｜b｜〉〉1（b〈0） the least upper bound of the number of isolated zeros of the related Abelian integrals I（h）=∮Γh（α＋βx2＋γx4）ydx is 2（counting the multiplicity） and this upper bound is a sharp one.展开更多
In this paper,the bifurcation of limit cycles for planar piecewise smooth systems is studied which is separated by a straight line.We give a new form of Abelian integrals for piecewise smooth systems which is simpler ...In this paper,the bifurcation of limit cycles for planar piecewise smooth systems is studied which is separated by a straight line.We give a new form of Abelian integrals for piecewise smooth systems which is simpler than before.In application,for piecewise quadratic system the existence of 10 limit cycles and 12 small-amplitude limit cycles is proved respectively.展开更多
In this paper,using the Abelian integral,we investigate the limit cycle bifurcation of two classes of non-smooth near-Hamiltonian systems,and obtain the maximum number of limit cycles of the system.
In this paper, we study a class of complete Abelian integral. We give an exact number and the upper bound of the number of zero points of the integral under some conditions.
文摘An upper bound B(n)≤ 12{7n+12((-1) n-1)} is derived for the number of zeros of Abelian integralsI(h)=∮ Γ h g(x,y)dy-f(x,y)dx on the open interval (-112,0)∪ (0,+∞), where Γ h is the compact component of the algebraic curve H(x,y)=12y 2+13x 3+14x 4=h,f(x,y) and g(x,y) are polynomials of x and y,n= max s{ deg f(x,y), deg g(x,y)} .
基金Supported by the National Natural Science Foundation of China(Grant No.12061016)the Applied Mathematics Center of GuangxiFoundation of Guangxi Technological College of Machinery and Electrcity(Grant No.2021YKYZ010).
文摘In this paper, we study the periodic wave propagation phenomenon in elastic waveguides modeled by a combined double-dispersive partial differential equation(PDE).The traveling wave ansazt transforms the PDE model into a perturbed integrable ordinary differential equation(ODE). The global bifurcation theory is applied for the perturbed ODE model to establish the existence and uniqueness of the limit cycle, which corresponds the periodic traveling wave for the PDE model. The main tool is the Abelian integral taken from Poincaré bifurcation theory. Simulation is carried out to verify the theoretical result.
文摘In this paper, the KP-MEW(2,2) equation is considered under a certain parametric condition. We prove that the equation has two isochronous centers under certain parametric conditions, and there exist two families of periodic solutions with equal period.
文摘Abstract This paper is devoted to the study of the period function for a class of reversible quadratic system x=-2xy,y=k-1-2kx＋（k＋1）x^2-1/2y^2.We determine the monotonicity of the period function for each k ∈ R. It is proved that the period function has at most one critical point.
基金Supported by National Natural Science Foundation of China(Grant No.11271046)
文摘In this paper,we consider Li′enard systems of the form dx/dt=y,dy/dt=x＋bx3-x5＋ε（α＋βx2＋γx4）y,where b∈R,0〈｜ε｜〈〈1,（α,β,γ）∈D∈R3 and D is bounded.We prove that for ｜b｜〉〉1（b〈0） the least upper bound of the number of isolated zeros of the related Abelian integrals I（h）=∮Γh（α＋βx2＋γx4）ydx is 2（counting the multiplicity） and this upper bound is a sharp one.
文摘In this paper,the bifurcation of limit cycles for planar piecewise smooth systems is studied which is separated by a straight line.We give a new form of Abelian integrals for piecewise smooth systems which is simpler than before.In application,for piecewise quadratic system the existence of 10 limit cycles and 12 small-amplitude limit cycles is proved respectively.
基金supported by the NNSF of China (10971139)China Postdoctoral Fund(2011M500615)Scientific Innovation Projection of Shanghai Education Department (11YZ225)
文摘In this paper,using the Abelian integral,we investigate the limit cycle bifurcation of two classes of non-smooth near-Hamiltonian systems,and obtain the maximum number of limit cycles of the system.
文摘In this paper, we study a class of complete Abelian integral. We give an exact number and the upper bound of the number of zero points of the integral under some conditions.
