Bifurcation mechanism and hybrid control strategy of a finance model with delays

Abstract

Establishing financial models or economic models to describe economic phenomena in real life has become a heated discussion in society at present. From a mathematical point of view, the exploration on dynamics of financial models or economic models is a valuable work. In this study, we build a new delayed finance model and explore the dynamical behavior containing existence and uniqueness, boundedness of solution, Hopf bifurcation, and Hopf bifurcation control of the considered delayed finance model. By virtue of fixed point theorem, we prove the existence and uniqueness of the solution to the considered delayed finance model. Applying a suitable function, we obtain the boundedness of the solutions for the considered delayed finance model. Taking advantage of the stability criterion and bifurcation argument of delayed differential equation, we establish a delay-independent condition ensuring the stability and generation of Hopf bifurcation of the involved delayed finance model. Exploiting hybrid controller including state feedback and parameter perturbation, we efficaciously adjust the stability region and the time of occurrence of Hopf bifurcation of the involved delayed finance model. The study manifests that time delay is a fundamental parameter in controlling stability region and the time of onset of Hopf bifurcation of the involved delayed finance model. To examine the soundness of established key results, computer simulation figures are concretely displayed. The derived conclusions of this study are perfectly new and has momentous theoretical value in economical operation.

Mathematical Modeling Reveals Mechanisms of Cancer-Immune Interactions Underlying Hepatocellular Carcinoma Development

“…This analysis helps in assessing local and global stability in biological systems. When dealing with a system exhibiting the same time delay, one may refer to the proof procedure outlined in Reference [43]. Conversely, for systems with different time delays, the findings and proof methods presented in References [44,45] can be applied.Additionally, by introducing periodic dynamics [46,47] through the incorporation of periodic components into the model, researchers can calculate important parameters such as the basic regeneration number and determine the possibilities of extinction and persistence of equilibrium solutions.…”