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

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arxiv 2107.03847 v1 pith:6QGIT7WP submitted 2021-07-08 math.NA cs.NA

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

classification math.NA cs.NA
keywords quadraticbilinearequationsystemdynamicalexistencesolutionapplications
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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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.

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