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

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.