Thu Dau Mot University Journal of Science

A study of fixed points and hopf bifurcation of hindmarsh-rose model

By Phan Văn Long Em
DOI: 10.37550/tdmu.EJS/2020.01.002


In this article, a class of Hindmarsh-Rose model is studied. First, all necessary conditions for the parameters of system are found in order to have one stable fixed point which presents the resting state for this famous model. After that, using the Hopf’s theorem proofs analytically the existence of a Hopf bifurcation, which is a critical point where a system’s stability switches and a periodic solution arises. More precisely, it is a local bifurcation in which a fixed point of a dynamical system loses stability, as a pair of complex conjugate eigenvalues cross the complex plane imaginary axis. Moreover, with the suitable assumptions for the dynamical system, a small-amplitude limit cycle branches from the fixed point.

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Publication Information


Thu Dau Mot University, Viet Nam

Honorary Editor-in-Chief and Chairman of the Editorial Board

Assoc. Prof. Nguyen Van Hiep

Deputy Editor-in-Chief

PhD. Trần Hạnh Minh Phương
Thu Dau Mot University

Editorial Board

Prof. Tran Van Doan
Fujen University, Taiwan
Prof. Zafar Uddin Ahmed
Vietnam National University Ho Chi Minh City

Prof.Dr. Phillip G.Cerny
The University of Manchester, United Kingdom
Prof. Ngo Van Le
University of Social Sciences and Humanities (VNU-HCM)

Prof. Bui The Cuong
Southern Institute of Social Sciences​​​​​​​
Prof. Le Quang Tri
Can Tho University

Assoc. Prof. Nguyen Van Duc
Animal Husbandry Association of Vietnam
Assoc. Prof. Ted Yuchung Liu
National Pingtung University, Taiwan

PhD. Anita Doraisami
Economics Monash University, Australia
Prof. Dr. Andrew Seddon
Asia Pacific University of Technology & innovation (APU)

Assoc. Prof. Le Tuan Anh
Thu Dau Mot University
Prof. Abtar Darshan Singh
Asia Pacific University, Malaysia

Prof.Dr. Ron W.Edwards
The University of Melbourne, Australia
Assoc. Prof. Hoang Xuan Nien
Thu Dau Mot University

PhD. Nguyen Duc Nghia
Vietnam National University Ho Chi Minh City
PhD. Bao Dat
Monash University (Australia)

PhD. Raqib Chowdhury
Monash University (Australia)
PhD. Nguyen Hoang Tuan
Thu Dau Mot University

PhD. Nguyen Thi Lien Thuong
Thu Dau Mot University


Nguyen Thi Man
Thu Dau Mot University