Rhythms of the brain: An examination of mixed mode oscillation approaches to the analysis of neurophysiological data

2008 ◽  
Vol 18 (1) ◽  
pp. 015115 ◽  
Author(s):  
Irina Erchova ◽  
David J. McGonigle
Keyword(s):  
Mixed Mode ◽  
Mode Oscillation ◽  
Neurophysiological Data ◽  
Mixed Mode Oscillation ◽  
The Brain

scholarly journals Chaotic and Mixed Mode Oscillation Scenarios in Semiconductor Devices: Generation and Synchronization

2012 ◽  
Vol 121 (1) ◽  
pp. 7-9 ◽  
Author(s):  
S.F. Abdalah ◽  
K. Al Naimee ◽  
M. Ciszak ◽  
F. Marino ◽  
R. Meucci ◽  
...  
Keyword(s):  
Mixed Mode ◽  
Semiconductor Devices ◽  
Mode Oscillation ◽  
Mixed Mode Oscillation

scholarly journals Periodically kicked feedforward chains of simple excitable FitzHugh-Nagumo neurons

2021 ◽  
Author(s):  
B. Ambrosio ◽  
S.M. Mintchev
Keyword(s):  
Numerical Investigation ◽  
Traveling Waves ◽  
Small Amplitude ◽  
Mixed Mode ◽  
Filtration Property ◽  
Periodic Traveling Waves ◽  
Mixed Mode Oscillations ◽  
Mode Oscillation ◽  
Existence And Stability ◽  
Mixed Mode Oscillation

Abstract This article communicates results on regular depolarization cascades in periodically-kicked feedforward chains of excitable two-dimensional FitzHugh-Nagumo systems driven by sufficiently strong excitatory forcing at the front node. The study documents a parameter exploration by way of changes to the forcing period, upon which the dynamics undergoes a transition from simple depolarization to more complex behavior, including the emergence of mixed-mode oscillations. Both rigorous studies and careful numerical observations are presented. In particular, we provide rigorous proofs for existence and stability of periodic traveling waves of depolarization, as well as the existence and propagation of a simple mixed-mode oscillation that features depolarization and refraction in alternating fashion. Detailed numerical investigation reveals a mechanism for the emergence of complex mixed-mode oscillations featuring a potentially high number of large amplitude voltage spikes interspersed by an occasional small amplitude reset that fails to cross threshold. Further careful numerical investigation provides insights into the propagation of this complex phenomenology in the downstream, where we see an effective filtration property of the network; the latter amounts to a successive reduction in the complexity of mixed-mode oscillations down the chain.

Bifurcation Structures of Nested Mixed-Mode Oscillations

2021 ◽  
Vol 31 (08) ◽  
pp. 2150121
Author(s):  
Munehisa Sekikawa ◽  
Naohiko Inaba
Keyword(s):  
Mixed Mode ◽  
Van Der Pol Oscillator ◽  
Van Der Pol ◽  
Mixed Mode Oscillations ◽  
Return Maps ◽  
Mode Oscillation ◽  
Mixed Mode Oscillation ◽  
Bifurcation Structures ◽  
First Return Maps ◽  
Strong Order

In recently published work [Inaba & Kousaka, 2020a; Inaba & Tsubone, 2020b], we discovered significant mixed-mode oscillation (MMO) bifurcation structures in which MMOs are nested. Simple mixed-mode oscillation-incrementing bifurcations (MMOIBs) are known to generate [Formula: see text] oscillations for successive [Formula: see text] between regions of [Formula: see text]- and [Formula: see text]-oscillations, where [Formula: see text] and [Formula: see text] are adjacent simple MMOs, e.g. [Formula: see text] and [Formula: see text], where [Formula: see text] is an integer. MMOIBs are universal phenomena of evidently strong order and have been studied extensively in chemistry, physics, and engineering. Nested MMOIBs are phenomena that are more complex, but have an even stronger order, generating chaotic MMO windows that include sequences [Formula: see text] for successive [Formula: see text], where [Formula: see text] and [Formula: see text] are adjacent MMOIB-generated MMOs, i.e. [Formula: see text] and [Formula: see text] for integer [Formula: see text]. Herein, we investigate the bifurcation structures of nested MMOIB-generated MMOs exhibited by a classical forced Bonhoeffer–van der Pol oscillator. We use numerical methods to prepare two- and one-parameter bifurcation diagrams of the system with [Formula: see text], and 3 for successive [Formula: see text] for the case [Formula: see text]. Our analysis suggests that nested MMOs could be widely observed and are clearly ordered phenomena. We then define the first return maps for nested MMOs, which elucidate the appearance of successively nested MMOIBs.

Analysis of mixed-mode oscillation-incrementing bifurcations generated in a nonautonomous constrained Bonhoeffer–van der Pol oscillator

2017 ◽  
Vol 353-354 ◽  
pp. 48-57 ◽  
Author(s):  
Takuji Kousaka ◽  
Yutsuki Ogura ◽  
Kuniyasu Shimizu ◽  
Hiroyuki Asahara ◽  
Naohiko Inaba
Keyword(s):  
Mixed Mode ◽  
Van Der Pol Oscillator ◽  
Van Der Pol ◽  
Mode Oscillation ◽  
Mixed Mode Oscillation
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