The author of this article considers a numerical method that uses high-precision calculations to construct approximations to attractors of dynamical systems of chaotic type with a quadratic right-hand side, as well as to find the vertical asymptotes of solutions of systems of explosive type. A special case of such systems is the population explosion model. A theorem on the existence of asymptotes is proved. The extension of the numerical method for piecewise smooth systems is described using the Chua system as an example, as well as systems with hysteresis.

翻译：本文作者考虑了一种数字方法,这种方法使用高精度计算法构建近似值,以吸引具有象形右侧的混乱型动态系统的吸引者,并寻找爆炸型系统溶液的垂直零点,这类系统的一个特殊情况是人口爆炸模型,证明了关于无粒子存在的理论,以Chua系统为例,并用歇斯底里系统为例,说明了小片光滑系统数字方法的延伸。