Global Stabilization of Delayed Feedback Financial System Involved in Advertisement under Impulsive Disturbance

Xinggui Li and Xinsong Yang ()
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Xinggui Li: Department of Mathematics, Chengdu Normal University, Chengdu 611130, China
Xinsong Yang: College of Electronics and Information Engineering, Sichuan University, Chengdu 610065, China

Mathematics, 2023, vol. 11, issue 9, 1-12

Abstract: Diffusion is an inevitable important factor in advertising dynamic systems. However, previous literature did not involve this important diffusion factor, and only involved the local stability of the advertising model. This paper develops a global stability criterion for the impulsive advertising dynamic model with a feedback term under the influence of diffusion. Since global stability requires the unique existence of equilibrium points, variational methods are employed to solve it in the infinite dimensional function space, and then a global stability criterion of the system is derived by way of the impulse inequality lemma and orthogonal decomposition of a class of Sobolev spaces. Numerical simulations verify the effectiveness of the proposed method.

Keywords: Neumann boundary value; delayed feedback; global stabilization; advertisement model; time-delayed reaction–diffusion system (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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