A quadratic dynamical system with practical applications is taken into considered. This system is transformed into a new bilinear system with Hadamard products by means of the implicit matrix structure. The corresponding quadratic bilinear equation is subsequently established via the Volterra series. Under proper conditions the existence of the solution to the equation is proved by using a fixed-point iteration.

翻译：考虑采用具有实际应用性的二次动态系统,通过隐含矩阵结构,将这一系统转化为新的双线系统,由Hadamard产品组成,随后通过Volterra系列确定相应的二次线性方程式,在适当条件下,通过使用固定点迭代来证明该方程式的解决方案的存在。