Noise-induced mixed-mode oscillations in a relaxation oscillator near the onset of a limit cycle

2008 ◽  
Vol 18 (1) ◽  
pp. 015111 ◽  
Author(s):  
Cyrill B. Muratov ◽  
Eric Vanden-Eijnden
Keyword(s):  
Limit Cycle ◽  
Mixed Mode ◽  
Relaxation Oscillator ◽  
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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