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

TL;DR

This paper investigates the existence of solutions to a quadratic bilinear equation derived from quadratic dynamical systems, using fixed-point methods under certain conditions, with implications for practical applications.

Contribution

It introduces a new approach to analyze quadratic bilinear equations from dynamical systems using fixed-point theory and matrix structures.

Findings

Existence of solutions established under specific conditions.

Transformation of quadratic dynamical systems into bilinear form.

Application of fixed-point iteration to prove solution existence.

Abstract

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.