Analysis of Two- and Three-Dimensional Fractional-Order Hindmarsh-Rose Type Neuronal Models

被引：0
作者：
Eva Kaslik
机构：
[1] Institute e-Austria Timisoara,Dept. of Mathematics and Computer Science
[2] West University of Timisoara,undefined
来源：
Fractional Calculus and Applied Analysis | 2017年 / 20卷
关键词：
Primary 26A33; Secondary 33E12; 34A08; 34K37; 35R11; 60G22; fractional-order; Hindmarsh-Rose model; Hodgkin-Huxley equations; neuron; neuronal activity; stability; Hopf bifurcation; bursting; slow-fast system;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
A theoretical analysis of two- and three-dimensional fractional-order Hindmarsh-Rose neuronal models is presented, focusing on stability properties and occurrence of Hopf bifurcations, with respect to the fractional order of the system chosen as bifurcation parameter. With the aim of exemplifying and validating the theoretical results, numerical simulations are also undertaken, which reveal rich bursting behavior in the three-dimensional fractional-order slow-fast system.
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页码：623 / 645
页数：22
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[21]   On the Three-Dimensional Fractional-Order Henon Map with Lorenz-Like Attractors [J].
Khennaoui, Amina-Aicha ;
Ouannas, Adel ;
Odibat, Zaid ;
Viet-Thanh Pham ;
Grassi, Giuseppe .
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2020, 30 (11)
[22]   Modified sliding mode synchronization of typical three-dimensional fractional-order chaotic systems [J].
Gao, Like ;
Wang, Zhihui ;
Zhou, Ke ;
Zhu, Wenji ;
Wu, Zhiding ;
Ma, Tiedong .
NEUROCOMPUTING, 2015, 166 :53-58
[23]   Three-dimensional chaotic autonomous van der pol-duffing type oscillator and its fractional-order form [J].
Kuiate, Gaetan Fautso ;
Kingni, Sifeu Takougang ;
Tamba, Victor Kamdoum ;
Talla, Pierre Kisito .
CHINESE JOURNAL OF PHYSICS, 2018, 56 (05) :2560-2573
[24]   Stability Analysis for a Fractional-Order Coupled FitzHugh-Nagumo-Type Neuronal Model [J].
Brandibur, Oana ;
Kaslik, Eva .
FRACTAL AND FRACTIONAL, 2022, 6 (05)
[25]   Dynamical analysis of two fractional-order SIQRA malware propagation models and their discretizations [J].
Manh Tuan Hoang .
RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO, 2023, 72 (01) :751-771
[26]   Three-dimensional implementation of multi-mode fractional-order elliptical perfect optical vortex arrays [J].
Kang, Xiangyu ;
Chen, Keyu ;
Wang, Guanxue ;
Zhang, Ning ;
Gao, Xiumin ;
Liu, Yi ;
Zhuang, Songlin .
OPTICS AND LASER TECHNOLOGY, 2024, 170
[27]   Analysis and numerical approximation of the fractional-order two-dimensional diffusion-wave equation [J].
Rafaqat, Kanza ;
Naeem, Muhammad ;
Akgul, Ali ;
Hassan, Ahmed M. ;
Abdullah, Farah Aini ;
Ali, Umair .
FRONTIERS IN PHYSICS, 2023, 11
[28]   TOPOLOGICAL DISSIPATIVE NONLINEAR MODES IN TWO- AND THREE-DIMENSIONAL GINZBURG-LANDAU MODELS WITH TRAPPING POTENTIALS [J].
Mihalache, D. .
ROMANIAN REPORTS IN PHYSICS, 2011, 63 (01) :9-24
[29]   A simple three-dimensional fractional-order chaotic system without equilibrium: Dynamics, circuitry implementation, chaos control and synchronization [J].
Viet-Thanh Pham ;
Kingni, Sifeu Takougang ;
Volos, Christos ;
Jafari, Sajad ;
Kapitaniak, Tomasz .
AEU-INTERNATIONAL JOURNAL OF ELECTRONICS AND COMMUNICATIONS, 2017, 78 :220-227
[30]   Three-dimensional chaotic autonomous system with only one stable equilibrium: Analysis, circuit design, parameter estimation, control, synchronization and its fractional-order form [J].
S. T. Kingni ;
S. Jafari ;
H. Simo ;
P. Woafo .
The European Physical Journal Plus, 129
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