Analysis of Dynamical Behaviors in a Continuous Chaotic System Without Šil'nikov Orbits

This paper discusses a simple yet interesting three-dimensional autonomous quadratic chaotic system, which has two fixed points of saddle-focus type but does not belong to the class of Sil'nikov type since there are neither homoclinic nor heteroclinic orbits. Dynamical behaviors of this chaotic system are investigated in detail through analyzing bifurcation routes, Lyapunov exponents and Poincare mappings. These investigations partially reveal the mechanism of how chaos in non-Sil'nikov type of systems is generated.