This article presents a hyperchaotic system of five-dimensional autonomous ODEs that has five cross-product nonlinearities. Under certain parametric conditions, it exhibits three different types of hyperchaotic and chaotic systems which correspond to six hyperchaotic attractors with a non-hyperbolic equilibrium line, four chaotic attractors with seventeen hyperbolic equilibria, and four chaotic attractors with only one hyperbolic equilibrium, respectively. The fundamental dynamics are analyzed theoretically and numerically, such as the onset of hyperchaos and chaos, routes to chaos, persistence of chaos, coexistence of attractors, periodic windows and bifurcations. It is particularly shown that the coexisting attractors of the 5D system inside the hypercone are symmetric. Some dynamical characteristics of these attractors are illustrated.

本文介绍了具有五个跨产品非线性的五维自治ODE的超混沌系统。在某些参数条件下，它表现出三种不同类型的超混沌和混沌系统，分别对应于六个具有非双曲平衡线的超混沌吸引子，四个具有十七个双曲平衡点的混沌吸引子和四个仅具有一个双曲平衡的混沌吸引子。从理论上和数字上分析了基本动力学，例如超混沌和混沌的发生，到混沌的路径，混沌的持续性，吸引子的共存，周期性窗口和分叉。特别表明5 D并存的吸引子超圆锥内部的系统是对称的。说明了这些吸引子的一些动力学特征。