Reconstruction of integrate-and-fire dynamics

2006 ◽  
pp. 63-75
Author(s):  
Timothy Sauer
Keyword(s):  
Fire Dynamics ◽  
Integrate And Fire

scholarly journals Three Different Ways Synchronization can Cause Contagion in Financial Markets

2018 ◽  
Author(s):  
Jorgen Vitting Andersen ◽  
Naji Masaad
Keyword(s):  
Decision Making ◽  
Financial Markets ◽  
Financial Market ◽  
Change Blindness ◽  
Market Performance ◽  
Large Change ◽  
Trading Strategies ◽  
Fire Dynamics ◽  
Integrate And Fire ◽  
Human Decision

We introduce tools to capture the dynamics of three different pathways, in which the synchronization of human decision making could lead to turbulent periods and contagion phenomena in financial markets. The first pathway is caused when stock market indices, seen as a set of coupled integrate-and-fire oscillators, synchronize in frequency. The integrate-and-fire dynamics happens due to "change blindness", a trait in human decision making where people have the tendency to ignore small changes, but take action when a large change happens. The second pathway happens due to feedback mechanisms between market performance and the use of certain (decoupled) trading strategies. The third pathway occurs through the effects of communication and its impact on human decision making. A model is introduced in which financial market performance has an impact on decision making through communication between people. Conversely, the sentiment created via communication has an impact on financial market performance.

STRUCTURE AND DYNAMICS: THE TRANSITION FROM NONEQUILIBRIUM TO EQUILIBRIUM IN INTEGRATE-AND-FIRE DYNAMICS

2012 ◽  
Vol 22 (07) ◽  
pp. 1250174 ◽  
Author(s):  
CESAR H. COMIN ◽  
JOÃO L. B. BATISTA ◽  
MATHEUS P. VIANA ◽  
LUCIANO DA F. COSTA ◽  
BRUNO A. N. TRAVENÇOLO ◽  
...  
Keyword(s):  
Systematic Approach ◽  
Local Level ◽  
Small World ◽  
Structural Features ◽  
Fire Dynamics ◽  
Integrate And Fire ◽  
Structure And Dynamics ◽  
Topological Features ◽  
Dynamical Features ◽  
Local Topology

The transient and equilibrium properties of dynamics unfolding in complex systems can depend critically on specific topological features of the underlying interconnections. In this work, we investigate such a relationship with respect to the integrate-and-fire dynamics emanating from a source node and an extended network model that allows control of the small-world feature as well as the length of the long-range connections. A systematic approach to investigate the local and global correlations between structural and dynamical features of the networks was adopted that involved extensive simulations (one and a half million cases) so as to obtain two-dimensional correlation maps. Smooth, but diverse surfaces of correlation values were obtained in all cases. Regarding the global cases, it has been verified that the onset avalanche time (but not its intensity) can be accurately predicted from the structural features within specific regions of the map (i.e. networks with specific structural properties). The analysis at local level revealed that the dynamical features before the avalanches can also be accurately predicted from structural features. This is not possible for the dynamical features after the avalanches take place. This is so because the overall topology of the network predominates over the local topology around the source at the stationary state.

scholarly journals Fundamental Limits of Forced Asynchronous Spiking with Integrate and Fire Dynamics

2017 ◽  
Vol 7 (1) ◽  
Author(s):  
Anirban Nandi ◽  
Heinz Schättler ◽  
Jason T. Ritt ◽  
ShiNung Ching
Keyword(s):  
Fire Dynamics ◽  
Fundamental Limits ◽  
Integrate And Fire

Traveling Waves of Excitation in Neural Field Models: Equivalence of Rate Descriptions and Integrate-and-Fire Dynamics

2002 ◽  
Vol 14 (7) ◽  
pp. 1651-1667 ◽  
Author(s):  
Daniel Cremers ◽  
Andreas V. M. Herz
Keyword(s):  
Traveling Waves ◽  
Neural Activity ◽  
Large Scale ◽  
Plane Waves ◽  
Network Connectivity ◽  
Microscopic Level ◽  
Mathematical Framework ◽  
Fire Dynamics ◽  
Integrate And Fire ◽  
Quantitative Results

Field models provide an elegant mathematical framework to analyze large-scale patterns of neural activity. On the microscopic level, these models are usually based on either a firing-rate picture or integrate-andfire dynamics. This article shows that in spite of the large conceptual differences between the two types of dynamics, both generate closely related plane-wave solutions. Furthermore, for a large group of models, estimates about the network connectivity derived from the speed of these plane waves only marginally depend on the assumed class of microscopic dynamics. We derive quantitative results about this phenomenon and discuss consequences for the interpretation of experimental data.

scholarly journals Three Different Ways Synchronization Can Cause Contagion in Financial Markets

Risks ◽  
2018 ◽  
Vol 6 (4) ◽  
pp. 104 ◽  
Author(s):  
Naji Massad ◽  
Jørgen Andersen
Keyword(s):  
Decision Making ◽  
Financial Markets ◽  
Financial Market ◽  
Change Blindness ◽  
Market Performance ◽  
Large Change ◽  
Fire Dynamics ◽  
Agent Based ◽  
Integrate And Fire ◽  
Human Decision

We introduce tools to capture the dynamics of three different pathways, in which the synchronization of human decision-making could lead to turbulent periods and contagion phenomena in financial markets. The first pathway is caused when stock market indices, seen as a set of coupled integrate-and-fire oscillators, synchronize in frequency. The integrate-and-fire dynamics happens due to “change blindness”, a trait in human decision-making where people have the tendency to ignore small changes, but take action when a large change happens. The second pathway happens due to feedback mechanisms between market performance and the use of certain (decoupled) trading strategies. The third pathway occurs through the effects of communication and its impact on human decision-making. A model is introduced in which financial market performance has an impact on decision-making through communication between people. Conversely, the sentiment created via communication has an impact on financial market performance. The methodologies used are: agent based modeling, models of integrate-and-fire oscillators, and communication models of human decision-making.

Solitary waves on manifolds of integrate-and-fire neurons

1998 ◽  
Vol 77 (5) ◽  
pp. 1575-1583
Author(s):  
David Horn, Irit Opher
Keyword(s):  
Solitary Waves ◽  
Integrate And Fire
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