Weigu Li
In this paper,we study a two-parameter family of systems Ec in which E0 as a contour consisting of a saddle point and two periodic motions of saddle type,i.e.,the situation is similar to that described by Lorenz equations for parameters b=8/3,σ=10,r=rl=24.06,and get some results concerning bifurcation phenomenon and dynamical behavior of the orbits of Ec in a small neighborhood of the contour for |ε| near zero.Thus,under a few natural assumptions which are verified numerically,we can explain some numerical results of Lorenz equations for parameters near the above values in a mathematically precise way,which is different from the methods of J.Guckenheimer et al.([3],[4]),by considering Lorenz equation as a one-or two-dimensional map.