Author:
Liu Zixin,Li Wenfang,Xu Changjin,Liu Chunfeng,Mu Dan,Xu Mengzhu,Ou Wei,Cui Qingyi
Abstract
AbstractEstablishing 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.
Funder
National Natural Science Foundation of China
Innovative Exploration Project of Guizhou University of Finance and Economics
Publisher
Springer Science and Business Media LLC
Subject
Algebra and Number Theory,Analysis
Reference28 articles.
1. Zhao, H.T., Lu, M.X., Zuo, J.M.: Anticontrol of Hopf bifurcation and control of chaos for a finance system through washout filters with time delay. Sci. World 2014, Article ID 983034 (2014)
2. Ma, J.H., Chen, Y.S.: Study for the bifurcation topological structure and the global complicated character of a kind of nonlinear finance system (I). Appl. Math. Mech. 22(11), 1119–1128 (2001)
3. Ma, J.H., Chen, Y.S.: Study for the bifurcation topological structure and the global complicated character of a kind of nonlinear finance system (II). Appl. Math. Mech. 22(12), 12361242 (2001)
4. Ma, C., Wang, X.Y.: Hopf bifurcation and topological horseshoe of a novel finance chaotic system. Commun. Nonlinear Sci. Numer. Simul. 17(2), 721–730 (2012)
5. Gao, Q.T., Ma, J.H.: Chaos and Hopf bifurcation of a finance system. Nonlinear Dyn. 58(1–2), 209–216 (2009)
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