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We seize some new dynamics of a Lorenz-like system: ẋ = a(y−x), ẏ = dy − xz, ż = −bz + fx + gxy, such as for the Hopf bifurcation, the behavior of non-isolated equilibria, the existence of singularly degenerate heteroclinic cycles and homoclinic and heteroclinic orbits. In particular, our new discovery is that the system has also two heteroclinic orbits for bg = 2a(f + g) and a > d > 0 other than known bg > 2a(f + g) and a > d > 0, whose proof is completely different from known case. All the theoretical results obtained are also verified by numerical simulations.

HOPF BIFURCATION AND NEW SINGULAR ORBITS COINED IN A LORENZ-LIKE SYSTEM