二次系统的二重极限环和以无限大分界线环分支出两个极限环的例子

EXAMPLES OF ONE DOUBLE LIMIT CYCLE OR TWO SINGLE LIMIT CYCLES JUMPING FROM AN INFINITE SEPARATRIX CYCLE IN A QUADRATIC SYSTEM

二次系统的二重极限环和以无限大分界线环分支出两个极限环的例子沈伯骞，何平（辽宁师范大学数学系，大连１１６０２２）（辽宁警官专科学校，大连１１６０３３）ＥＸＡＭＰＬＥＳＯＦＯＮＥＤＯＵＢＬＥＬＩＭＩＴＣＹＣＬＥＯＲＴＷＯＳＩＮＧＬＥＬＩＭＩＴＣＹＣＬＥ...

In this paper we use the Poincare bifurcation theory to prove that there may be just one double limit cycle or just two single limit cycles jumping out of the periodic cycle region in a quadratic system, and that there may be just one double limit cycle or just two single limit cycles jumping from an infinite separatrix cycle with only one infinite critical point in a quadratic system. And we give respective specific examples for them.