Order in chaos: Structure of chaotic invariant sets of square-wave neuron models

2021 ◽  
Vol 31 (4) ◽  
pp. 043108
Author(s):  
Sergio Serrano ◽  
M. Angeles Martínez ◽  
Roberto Barrio
Keyword(s):  
Invariant Sets ◽  
Neuron Models ◽  
Square Wave

Spiking Neuron Models

2002 ◽  
Author(s):  
Wulfram Gerstner ◽  
Werner M. Kistler
Keyword(s):  
Spiking Neuron ◽  
Neuron Models ◽  
Spiking Neuron Models

Square Wave Jerks

2005 ◽  
Vol 222 (S 3) ◽  
Author(s):  
K Hassan ◽  
K Bornemann ◽  
R Effert
Keyword(s):  
Square Wave

Partial Discharge Activity of Inter-turn Insulation under Different Parameters of Square Wave Voltage

2009 ◽  
Vol 129 (12) ◽  
pp. 922-930 ◽  
Author(s):  
Kai Zhou ◽  
Guangning Wu ◽  
Xiaoxia Guo ◽  
Liren Zhou ◽  
Tao Zhang
Keyword(s):  
Partial Discharge ◽  
Square Wave ◽  
Discharge Activity ◽  
Turn Insulation

Action-Minimizing Curves for Tonelli Lagrangians

2017 ◽  
Author(s):  
Alfonso Sorrentino
Keyword(s):  
Critical Value ◽  
The Other ◽  
Invariant Sets ◽  
Simple Pendulum ◽  
New Concepts ◽  
Peierls Barrier ◽  
Average Action

This chapter discusses the notion of action-minimizing orbits. In particular, it defines the other two families of invariant sets, the so-called Aubry and Mañé sets. It explains their main dynamical and symplectic properties, comparing them with the results obtained in the preceding chapter for the Mather sets. The relation between these new invariant sets and the Mather sets is described. As a by-product, the chapter introduces the Mañé's potential, Peierls' barrier, and Mañé's critical value. It discusses their properties thoroughly. In particular, it highlights how this critical value is related to the minimal average action and describes these new concepts in the case of the simple pendulum.

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