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
As a continuation of,the author studies the limit cycle bifurcation around the focus S_(1)other than O(0,0)for the system(1)asδvaries.A conjecture on the mon-existence of limit cycles around S_(1),and another one on ...As a continuation of,the author studies the limit cycle bifurcation around the focus S_(1)other than O(0,0)for the system(1)asδvaries.A conjecture on the mon-existence of limit cycles around S_(1),and another one on the non-coexistence of limit cycles ariund both O and S_(1)are given,together with some numerical examples.展开更多
By using the generalized PoincarE index theorem it is proved that if the n2 critical points of an n-polynomial system form a configuration of type (2n -1) - (2n - 3) +(2n- 5) -…+ (- 1 )n- 1, and the 2n -1 outmost ant...By using the generalized PoincarE index theorem it is proved that if the n2 critical points of an n-polynomial system form a configuration of type (2n -1) - (2n - 3) +(2n- 5) -…+ (- 1 )n- 1, and the 2n -1 outmost anti-saddles form the venices of a convex (2n -1)-polygon, then among these 2n-1 anti-saddles at least one must be a node.展开更多
Qualitative properties of critical points, integral lines and limit cycles are studied. Interesting relations between quantities characterizing local properties and those characterizing global properties are obtained.
In this paper we study the variation of limit cycles around different foci when a coefficient in the equation of the quadratic differential system varies.
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As a continuation of,the author studies the limit cycle bifurcation around the focus S_(1)other than O(0,0)for the system(1)asδvaries.A conjecture on the mon-existence of limit cycles around S_(1),and another one on the non-coexistence of limit cycles ariund both O and S_(1)are given,together with some numerical examples.
文摘By using the generalized PoincarE index theorem it is proved that if the n2 critical points of an n-polynomial system form a configuration of type (2n -1) - (2n - 3) +(2n- 5) -…+ (- 1 )n- 1, and the 2n -1 outmost anti-saddles form the venices of a convex (2n -1)-polygon, then among these 2n-1 anti-saddles at least one must be a node.
文摘Qualitative properties of critical points, integral lines and limit cycles are studied. Interesting relations between quantities characterizing local properties and those characterizing global properties are obtained.
文摘In this paper we study the variation of limit cycles around different foci when a coefficient in the equation of the quadratic differential system varies.
