By extending the extreme learning machine by additional control inputs, we achieved almost complete reproduction of bifurcation structures of dynamical systems. The learning ability of the proposed neural network system is striking in that the entire structure of the bifurcations of a target one-parameter family of dynamical systems can be nearly reproduced by training on transient dynamics using only a few parameter values. Moreover, we propose a mechanism to explain this remarkable learning ability and discuss the relationship between the present results and similar results obtained by Kim et al.

翻译：通过为极限学习机增加额外的控制输入，我们实现了对动力系统分岔结构的近乎完整复现。所提出的神经网络系统的学习能力令人瞩目，仅需使用少数参数值对瞬态动力学进行训练，即可近乎复现目标单参数动力系统族的分岔整体结构。此外，我们提出了一种机制来解释这种卓越的学习能力，并讨论了本研究结果与Kim等人所获类似结果之间的关系。