Mean-Field Population Dynamics of Spiking Neurons with Random Synaptic Delays

2002 ◽  
pp. 111-116 ◽  
Author(s):  
Maurizio Mattia ◽  
Paolo Del Giudice
Keyword(s):  
Population Dynamics ◽  
Mean Field ◽  
Spiking Neurons ◽  
Field Population

scholarly journals A Mean-Field Description of Bursting Dynamics in Spiking Neural Networks with Short-Term Adaptation

2019 ◽  
Author(s):  
R. Gast ◽  
H. Schmidt ◽  
T.R. Knösche
Keyword(s):  
Population Dynamics ◽  
Phase Transitions ◽  
Neurological Disorders ◽  
Mean Field ◽  
Population Level ◽  
Spiking Neurons ◽  
Short Term ◽  
Adaptation Mechanisms ◽  
Neural Communication ◽  
Short Term Adaptation

Bursting plays an important role in neural communication. At the population level, macro-scopic bursting has been identified in populations of neurons that do not express intrinsic bursting mechanisms. For the analysis of such phase transitions, mean-field descriptions of macroscopic bursting behavior pose a valuable tool. In this article, we derive mean-field descriptions of populations of spiking neurons in which collective bursting behavior arises via short-term adaptation mechanisms. Specifically, we consider synaptic depression and spike-frequency adaptation in networks of quadratic integrate-and-fire neurons. We characterize the emerging bursting behavior using bifurcation analysis and validate our mean-field derivations by comparing the microscopic and macroscopic descriptions of the population dynamics. Hence, we provide mechanistic descriptions of phase transitions between bursting and non-bursting population dynamics which play important roles in both healthy neural communication and neurological disorders.

scholarly journals Population dynamics with spatial structure and an Allee effect

2020 ◽  
Author(s):  
Anudeep Surendran ◽  
Michael Plank ◽  
Matthew Simpson
Keyword(s):  
Population Dynamics ◽  
Spatial Structure ◽  
Short Range ◽  
Allee Effect ◽  
Mean Field ◽  
Mean Field Approximation ◽  
Continuum Approximation ◽  
Spatial Moment ◽  
Mean Field Models ◽  
The Mean

AbstractAllee effects describe populations in which long-term survival is only possible if the population density is above some threshold level. A simple mathematical model of an Allee effect is one where initial densities below the threshold lead to population extinction, whereas initial densities above the threshold eventually asymptote to some positive carrying capacity density. Mean field models of population dynamics neglect spatial structure that can arise through short-range interactions, such as short-range competition and dispersal. The influence of such non mean-field effects has not been studied in the presence of an Allee effect. To address this we develop an individual-based model (IBM) that incorporates both short-range interactions and an Allee effect. To explore the role of spatial structure we derive a mathematically tractable continuum approximation of the IBM in terms of the dynamics of spatial moments. In the limit of long-range interactions where the mean-field approximation holds, our modelling framework accurately recovers the mean-field Allee threshold. We show that the Allee threshold is sensitive to spatial structure that mean-field models neglect. For example, we show that there are cases where the mean-field model predicts extinction but the population actually survives and vice versa. Through simulations we show that our new spatial moment dynamics model accurately captures the modified Allee threshold in the presence of spatial structure.

scholarly journals (Sub)Optimal feedback control of mean field multi-population dynamics

2018 ◽  
Vol 51 (3) ◽  
pp. 86-91 ◽  
Author(s):  
Giacomo Albi ◽  
Dante Kalise
Keyword(s):  
Population Dynamics ◽  
Feedback Control ◽  
Mean Field ◽  
Optimal Feedback Control ◽  
Optimal Feedback

A mathematical model of field population dynamics of the southern pine beetle, dendroctonus frontalis

1981 ◽  
Vol 13 (4) ◽  
pp. 261-281 ◽  
Author(s):  
Richard M. Feldman ◽  
Guy L. Curry ◽  
Robert N. Coulson
Keyword(s):  
Mathematical Model ◽  
Population Dynamics ◽  
Dendroctonus Frontalis ◽  
Field Population ◽  
Southern Pine Beetle ◽  
Southern Pine ◽  
Pine Beetle

Field Population Dynamics of Soybean Cyst Nematode on Resistant and Susceptible Soybeans and Their Blends

Crop Science ◽  
1995 ◽  
Vol 35 (3) ◽  
pp. 703-707 ◽  
Author(s):  
M. K. Wallace ◽  
J. H. Orf ◽  
W. C. Stienstra
Keyword(s):  
Population Dynamics ◽  
Soybean Cyst Nematode ◽  
Cyst Nematode ◽  
Field Population

scholarly journals Population Dynamics of Spiking Neurons: Fast Transients, Asynchronous States, and Locking

2000 ◽  
Vol 12 (1) ◽  
pp. 43-89 ◽  
Author(s):  
Wulfram Gerstner
Keyword(s):  
Integral Equation ◽  
Population Dynamics ◽  
Small Amplitude ◽  
Spiking Neurons ◽  
Linear Filter ◽  
Population Activity ◽  
Integrate And Fire ◽  
Fast Transients ◽  
The Stability ◽  
Fire Type

An integral equation describing the time evolution of the population activity in a homogeneous pool of spiking neurons of the integrate-and-fire type is discussed. It is analytically shown that transients from a state of incoherent firing can be immediate. The stability of incoherent firing is analyzed in terms of the noise level and transmission delay, and a bifurcation diagram is derived. The response of a population of noisy integrate-and-fire neurons to an input current of small amplitude is calculated and characterized by a linear filter L. The stability of perfectly synchronized “locked” solutions is analyzed.

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