Dynamical Analysis of a Nonlinear Financial System with Computational Algebra Methods

Yıl 2020, , 1142 - 1154, 31.01.2020

Orhan Ozgur Aybar

https://doi.org/10.29130/dubited.644487

Öz

This
paper presents algebraic invariants and bifurcation analysis of a nonlinear
financial system. We focus on the local stability of the equilibrium points of
this system and find the suitable values of parameters for Hopf Bifurcation.
Finally, we investigate the invariants to show the general behaviour.

Anahtar Kelimeler

Stability, Invariants, Bifurcation Analysis

Destekleyen Kurum

TÜBİTAK

Proje Numarası

119F017

Teşekkür

This work is supported by the Scientific and Technological Research Council of Turkey (TUBITAK) under the project number 119F017.

Doğrusal Olmayan Bir Finansal Sistemin Hesaplamalı Cebir Metotlarıyla Dinamik Analizi

Öz

Bu çalışmada doğrusal
olmayan bir finansal sistemin çatallanma analizi ve cebirsel değişmezleri
sunulmaktadır. Sistemin denge noktalarının kararlılık analizi ve Hopf
çatallanmasının göründüğü parametre değerlerine odaklanılmıştır. Son olarak
genel davranışın gösterilmesi için değişmezler incelenmiştir.

 

Anahtar Kelimeler:
Kararlılık Analizi, Değişmezler, Çatallanma Analizi

Anahtar Kelimeler

Kararlılık Analizi, Değişmezler, Çatallanma Analizi

Proje Numarası

119F017

Kaynakça

• [1] J. H., Ma and Y. S. Chen, “Study for the bifurcation topological structure and the global complicated character of a kind of nonlinear finance system (I),” Applied Mathematics and Mechanics, vol. 22, no. 11, pp. 1240–1251, 2001.
• [2] J. H., Ma and Y. S. Chen, “Study for the bifurcation topological structure and the global complicated character of a kind of nonlinear finance system (II),” Applied Mathematics and Mechanics, vol. 22, no. 12, pp. 1375–1382, 2001.
• [3] H. Yu, G. Cai and Y. Li, “Dynamic analysis and control of a new hyperchaotic finance system,” Nonlinear Dyn, vol. 67, pp. 2171–2182, 2012.
• [4] O. I. Tacha, Ch. K. Volos, I. M. Kyprianidis, I. N. Stouboulos, S. Vaidyanathan and V. -T. Pham, “Analysis, adaptive control and circuit simulation of a novel nonlinear finance system,” Applied Mathematics and Computation, vol. 276, pp. 200–217, 2016.
• [5] A. Hajipour, M. Hajipour, D. Baleanu, “On the adaptive sliding mode controller for a hyperchaotic fractional-order financial system,” Physica A, vol. 497, pp. 139–153, 2018.
• [6] W. C. Chen, “Dynamics and control of a financial system with time-delayed feedbacks,” Chaos, Solitons and Fractals, vol. 37, pp. 1198–1207, 2008.
• [7] V. G. Romanovski and D. S. Shafer, The Center and Cyclicity Problems: A Computational Algebra Approach, Basel, Birkhäuser, 2009.
• [8] I. Kusbeyzi Aybar, O. O. Aybar, B. Fercec, V. G. Romanovski, S. S. Samal and A. Weber, “Investigation of invariants of a chemical reaction system with algorithms of computer algebra”, MATCH Commun. Math. Comput. Chem., vol. 74, no. 3, pp. 465-480, 2015.
• [9] Murilo R. Candido, C. Valls, and Jaume Llibre, “Invariant Algebraic Surfaces and Hopf Bifurcation of a Finance Model”, International Journal of Bifurcation and Chaos, vol. 28, no. 12, pp.1850150, 2018.