【摘 要】
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The codimension 3 bifurcations associated with a heteroclinic loop formed with two saddle-foci (one has a pair of image eigenvalues) and two of their hetero
【机 构】
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Department of Mathematics, East China Normal University
【出 处】
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the 2nd Shanghai International Symposium on NOnlinear Scienc
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The codimension 3 bifurcations associated with a heteroclinic loop formed with two saddle-foci (one has a pair of image eigenvalues) and two of their heteroclinic orbits are considered in the 3-dimensional space.It is proved that,in a neighborhood of the heteroclinic loop,there are countably infinite 1-homoclinic orbits and l-heteroclinic orbits.Meanwhile,under a transversal condition,the existence of infinitely many heterclinic orbits joining two saddle-foci.1-and 3/2-heterclinic loops connecting a sddle-focus and a limit cycle produced from Hopf bifurcation,and 1-homoclinic orbits approaching the limit cycle or a sddle-focus are obtained,and the bifurcation surfaces and the existence regions are also given.
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