中文摘要：

构造一个仅含单一非线性立方项且维数可变的广义映像系统，该系统正性Lyapunov指数的个数随其维数增加而增加，可从低维混沌向高维超混沌过渡．利用Jury准则，解析广义立方映像系统从2维到4维的情况下，其不动点附近的局部稳定性，通过数值计算揭示该系统的动力学特征和规律．

英文摘要：

A generalized cubic map with alterable dimension was formulated. This map compromises only one nonlinear cubic term. The number of its positive Lyapunov exponents is increased with the growth of the map dimension accompanied by the transition from chaos to hyperchaos state. The stability of the cubic map from two dimensions to four dimensions was analyzed using the Jury rules. The dynamical characteristic of this cubic map was also deter- mined by numerical computations.