On a Class of Semilocal Bifurcations of Lorenz Type

<正> In this paper, we study a two-parameter family of systems Eε in which EO has acontour consisting of a saddle point and two periodic motions of saddle type, i.e., the situation issimilar 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 orbitsof Eε in a small neighborhood of the contour for |ε| near zero. Thus, under a few naturalassumptions which are verined numerically. we can explain some numerical results of Lorenzequations for parameters near the above values in a mathematically precise way, which is differentfrom the methods of J. Guckenheimer et al.（[3],[4]）,by considering Lorenz equation as a one--ortwo--dimensional map.