By making use of bifurcation analysis and continuation method, the authors discuss the exact number of positive solutions for a class of perturbed equations. The nonlinearities concerned are the so-called convex-conca...By making use of bifurcation analysis and continuation method, the authors discuss the exact number of positive solutions for a class of perturbed equations. The nonlinearities concerned are the so-called convex-concave functions and their behaviors may be asymptotic sublinear or asymptotic linear. Moreover, precise global bifurcation diagrams are obtained.展开更多
For the quadratic system: x=-y+δx + lx2 + ny2, y=x(1+ax-y) under conditions -1<l<0,n+l - 1>0 the author draws in the (a, ()) parameter plane the global bifurcationdiagram of trajectories around O(0,0). Notic...For the quadratic system: x=-y+δx + lx2 + ny2, y=x(1+ax-y) under conditions -1<l<0,n+l - 1>0 the author draws in the (a, ()) parameter plane the global bifurcationdiagram of trajectories around O(0,0). Notice that when na2+l < 0 the system has one saddleN(0,1/n) and three anti-saddles.展开更多
The quasi-periodic perturbation for the Duffing's equation with two external forcing terms has been discussed. The second order averaging method and sub-harmonic Melnikov's method through the medium of the ave...The quasi-periodic perturbation for the Duffing's equation with two external forcing terms has been discussed. The second order averaging method and sub-harmonic Melnikov's method through the medium of the averaging mrthod have been applied to detect the existence of quasiperiodic solutions and sub-harmonic bifurcation for the system. Sub-harmonic bifurcation curves are given by using numerical computation for sub-harmonic Melnikov's function.展开更多
基金supported by the Foundation of Shanghai Municipal Education Commission (No. 06DZ004).
文摘By making use of bifurcation analysis and continuation method, the authors discuss the exact number of positive solutions for a class of perturbed equations. The nonlinearities concerned are the so-called convex-concave functions and their behaviors may be asymptotic sublinear or asymptotic linear. Moreover, precise global bifurcation diagrams are obtained.
基金Project supported by the National Natural Science Foundation of China
文摘For the quadratic system: x=-y+δx + lx2 + ny2, y=x(1+ax-y) under conditions -1<l<0,n+l - 1>0 the author draws in the (a, ()) parameter plane the global bifurcationdiagram of trajectories around O(0,0). Notice that when na2+l < 0 the system has one saddleN(0,1/n) and three anti-saddles.
文摘The quasi-periodic perturbation for the Duffing's equation with two external forcing terms has been discussed. The second order averaging method and sub-harmonic Melnikov's method through the medium of the averaging mrthod have been applied to detect the existence of quasiperiodic solutions and sub-harmonic bifurcation for the system. Sub-harmonic bifurcation curves are given by using numerical computation for sub-harmonic Melnikov's function.
