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A quadratic dynamical system with practical applications is taken intoconsidered. This system is transformed into a new bilinear system with Hadamardproducts by means of the implicit matrix structure. The corresponding quadraticbilinear equation is subsequently established via the Volterra series. Underproper conditions the existence of the solution to the equation is proved byusing a fixed-point iteration.

Existence of The Solution to The Quadratic Bilinear Equation Arising from A Class of Quadratic Dynamical Systems