On the Darboux Integrability of the Hindmarsh–Rose Burster

被引：0
|
作者：
Jaume LLIBRE [1 ]
Cludia VALLS [2 ]
机构：
[1] Departament de Matemàtiques, Universitat Autònoma de Barcelona
[2] Departamento de Matem′atica, Instituto Superior Técnico,Universidade Técnica de
来源：
Acta Mathematica Sinica | 2018年 / 34卷 / 06期
关键词：
D O I：
暂无
中图分类号：
O175 [微分方程、积分方程];
学科分类号：
070104 ;
摘要：
We study the Hindmarsh–Rose burster which can be described by the differential system = y-x3+ bx2+ I-z,  = 1-5 x2-y, z = μ(s（x-x0）-z),where b, I, μ, s, x0 are parameters. We characterize all its invariant algebraic surfaces and all its exponential factors for all values of the parameters. We also characterize its Darboux integrability in function of the parameters. These characterizations allow to study the global dynamics of the system when such invariant algebraic surfaces exist.
引用
收藏
页码：947 / 958
页数：12
相关论文
共 50 条
  • [31] Hindmarsh-Rose neuron model with memristors
    Usha, K.
    Subha, P. A.
    BIOSYSTEMS, 2019, 178 : 1 - 9
  • [32] Multistability in networks of Hindmarsh-Rose neurons
    Erichsen, R., Jr.
    Brunnet, L. G.
    PHYSICAL REVIEW E, 2008, 78 (06):
  • [33] Shrimp hubs in the Hindmarsh-Rose model
    Stenzinger, Rafael V.
    Oliveira, Vinicius Luz
    Tragtenberg, M. H. R.
    CHAOS, 2025, 35 (02)
  • [34] Parameter Estimation for Hindmarsh-Rose Neurons
    Fradkov, Alexander L.
    Kovalchukov, Aleksandr
    Andrievsky, Boris
    ELECTRONICS, 2022, 11 (06)
  • [35] Nonlinear feedback coupling in Hindmarsh–Rose neurons
    Sunsu Kurian Thottil
    Rose P. Ignatius
    Nonlinear Dynamics, 2017, 87 : 1879 - 1899
  • [36] Synchronization in Networks of Hindmarsh-Rose Neurons
    Checco, Paolo
    Righero, Marco
    Biey, Mario
    Kocarev, Ljupco
    IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS, 2008, 55 (12) : 1274 - 1278
  • [37] CANARDS EXISTENCE IN THE HINDMARSH-ROSE MODEL
    Ginoux, Jean-Marc
    Llibre, Jaume
    Tchizawa, Kiyoyuki
    MATHEMATICAL MODELLING OF NATURAL PHENOMENA, 2019, 14 (04)
  • [38] Dynamics of Hindmarsh-Rose diffusive system
    Pan, Cuiyu
    Liu, Aimin
    Liu, Yongjian
    NONLINEAR DYNAMICS, 2025, 113 (02) : 1623 - 1635
  • [39] Exponential factors and Darboux integrability for the Rossler system
    Zhang, X
    INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2004, 14 (12): : 4275 - 4283
  • [40] Darboux polynomials and algebraic integrability of the Chen system
    Lu, Tinghua
    Zhang, Xiang
    INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2007, 17 (08): : 2739 - 2748
12345