Mixed-mode oscillations and the bifurcation mechanism for a Filippov-type dynamical system

Pramana ◽  
2019 ◽  
Vol 94 (1) ◽  
Author(s):  
Miao Peng ◽  
Zhengdi Zhang ◽  
Zifang Qu ◽  
Qinsheng Bi
Keyword(s):  
Dynamical System ◽  
Mixed Mode ◽  
Bifurcation Mechanism ◽  
Mixed Mode Oscillations ◽  
Filippov Type

Mixed mode oscillations as well as the bifurcation mechanism in a Duffing’s oscillator with two external periodic excitations

2019 ◽  
Vol 62 (10) ◽  
pp. 1816-1824
Author(s):  
XiaoFang Zhang ◽  
JianKang Zheng ◽  
GuoQing Wu ◽  
QinSheng Bi
Keyword(s):  
Mixed Mode ◽  
Bifurcation Mechanism ◽  
Mixed Mode Oscillations

scholarly journals Mixed-Mode Oscillations Based on Complex Canard Explosion in a Fractional-Order Fitzhugh-Nagumo Model.

2020 ◽  
Vol 5 (2) ◽  
pp. 239-256
Author(s):  
René Lozi ◽  
Mohammed-Salah Abdelouahab ◽  
Guanrong Chen
Keyword(s):  
Dynamical System ◽  
Fixed Point ◽  
Fractional Order ◽  
Small Amplitude ◽  
Mixed Mode ◽  
Complex Dynamics ◽  
Search Algorithm ◽  
Two Dimensional ◽  
Mixed Mode Oscillations ◽  
Autonomous Dynamical System

AbstractThis article highlights particular mixed-mode oscillations (MMO) based on canard explosion observed in a fractional-order Fitzhugh-Nagumo (FFHN) model. In order to rigorously analyze the dynamics of the FFHN model, a recently introduced mathematical notion, the Hopf-like bifurcation (HLB), which provides a precise definition for the change between a fixed point and an S−asymptotically T−periodic solution, is used. The existence of HLB in this FFHN model is proved and the appearance of MMO based on canard explosion in the neighborhoods of such HLB points are numerically investigated using a new algorithm: the global-local canard explosion search algorithm. This MMO is constituted of various patterns of solutions with an increasing number of small-amplitude oscillations when two key parameters of the FFHN model are varied simultaneously. On the basis of such numerical experiment, it is conjectured that chaos could occur in a two-dimensional fractional-order autonomous dynamical system, with the fractional-order close to one. Therefore, this very simple two-dimensional FFHN model, presents an incredible ability to mimic the complex dynamics of neurons.

Mixed Mode Oscillations (MMOs)

2021 ◽  
Author(s):  
Zdzislaw Trzaska
Keyword(s):  
Mixed Mode ◽  
Mixed Mode Oscillations

scholarly journals Complexity of a Peroxidase-Oxidase Reaction Model

2021 ◽  
Author(s):  
Jason Gallas ◽  
Marcus Hauser ◽  
Lars Folke Olsen
Keyword(s):  
Chemical Reaction ◽  
Mixed Mode ◽  
Period Doubling ◽  
Reaction Model ◽  
Chaotic Behaviour ◽  
Mixed Mode Oscillations ◽  
Oscillating Reaction ◽  
Oxidase Reaction

The peroxidase-oxidase oscillating reaction was the first (bio)chemical reaction to show chaotic behaviour. The reaction is rich in bifurcation scenarios, from period-doubling to peak-adding mixed mode oscillations. Here, we study...

Bursting patterns and mixed-mode oscillations in reduced Purkinje model

2018 ◽  
Vol 32 (05) ◽  
pp. 1850043 ◽  
Author(s):  
Feibiao Zhan ◽  
Shenquan Liu ◽  
Jing Wang ◽  
Bo Lu
Keyword(s):  
Purkinje Cell ◽  
Mixed Mode ◽  
Cell Model ◽  
Dynamical Behavior ◽  
Characteristic Index ◽  
Mixed Mode Oscillations ◽  
Codimension One ◽  
Bifurcation Phenomenon ◽  
Lyapunov Coefficient ◽  
Potential Link

Bursting discharge is a ubiquitous behavior in neurons, and abundant bursting patterns imply many physiological information. There exists a closely potential link between bifurcation phenomenon and the number of spikes per burst as well as mixed-mode oscillations (MMOs). In this paper, we have mainly explored the dynamical behavior of the reduced Purkinje cell and the existence of MMOs. First, we adopted the codimension-one bifurcation to illustrate the generation mechanism of bursting in the reduced Purkinje cell model via slow–fast dynamics analysis and demonstrate the process of spike-adding. Furthermore, we have computed the first Lyapunov coefficient of Hopf bifurcation to determine whether it is subcritical or supercritical and depicted the diagrams of inter-spike intervals (ISIs) to examine the chaos. Moreover, the bifurcation diagram near the cusp point is obtained by making the codimension-two bifurcation analysis for the fast subsystem. Finally, we have a discussion on mixed-mode oscillations and it is further investigated using the characteristic index that is Devil’s staircase.

Intermittency, Secondary Bifurcation and Mixed Mode Oscillations in a Swirl-Stabilized Annular Combustor: Experiments and Modeling

2021 ◽  
Author(s):  
Samarjeet Singh ◽  
Amitesh Roy ◽  
K V Reeja ◽  
Asalatha A. S. Nair ◽  
Swetaprovo Chaudhuri ◽  
...  
Keyword(s):  
Mixed Mode ◽  
Mixed Mode Oscillations ◽  
Annular Combustor ◽  
Secondary Bifurcation

One variable map prediction of Belousov–Zhabotinskii mixed mode oscillations

1984 ◽  
Vol 80 (11) ◽  
pp. 5610-5615 ◽  
Author(s):  
John Rinzel ◽  
Ira B. Schwartz
Keyword(s):  
Mixed Mode ◽  
Mixed Mode Oscillations
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