Hopf Bifurcations in a Delayed Microscopic Model of Credit Risk Contagion

Authors

Carlo Bianca, Sorbonne Universit´es, UPMC Univ Paris 06, UMR 7600, Laboratoire de Physique Th´eorique de la Mati`ere Condens´ee, 4, place Jussieu, case courrier 121, 75252 Paris cedex 05, France\\ CNRS, UMR 7600 LPTMC, Paris, FranceFollow
Luca Guerrini, Polytechnic University of Marche, Department of Management, 60121 Ancona, ItalyFollow

Author Country (or Countries)

France

Abstract

This paper is concerned with the proof of the existence of Hopf bifurcations in a mathematical model recently proposed in [T. Chen, X. Li, and J. He, Abstract and Applied Analysis 2014, 456764 (2014)] for understanding the complex stochastic dynamics phenomena of credit risk contagion in the financial market. Specifically the model consists in an ordinary differential equation with time-delay. Moreover, by using the normal form theory and center manifold argument, the stability, direction, and period of bifurcating periodic solutions are gained.

Recommended Citation

Bianca, Carlo and Guerrini, Luca (2015) "Hopf Bifurcations in a Delayed Microscopic Model of Credit Risk Contagion," Applied Mathematics & Information Sciences: Vol. 09: Iss. 3, Article 44.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol09/iss3/44