Chaos in small networks of theta neurons

2018 ◽  
Vol 28 (7) ◽  
pp. 073101
Author(s):  
Carlo R. Laing
Keyword(s):  
Theta Neurons

scholarly journals Complete Classification of the Macroscopic Behavior of a Heterogeneous Network of Theta Neurons

2013 ◽  
Vol 25 (12) ◽  
pp. 3207-3234 ◽  
Author(s):  
Tanushree B. Luke ◽  
Ernest Barreto ◽  
Paul So
Keyword(s):  
Limit Cycle ◽  
Heterogeneous Network ◽  
Mean Field ◽  
Complete Classification ◽  
Field Variable ◽  
Equilibrium States ◽  
Type I ◽  
Large Network ◽  
Theta Neurons

We design and analyze the dynamics of a large network of theta neurons, which are idealized type I neurons. The network is heterogeneous in that it includes both inherently spiking and excitable neurons. The coupling is global, via pulselike synapses of adjustable sharpness. Using recently developed analytical methods, we identify all possible asymptotic states that can be exhibited by a mean field variable that captures the network's macroscopic state. These consist of two equilibrium states that reflect partial synchronization in the network and a limit cycle state in which the degree of network synchronization oscillates in time. Our approach also permits a complete bifurcation analysis, which we carry out with respect to parameters that capture the degree of excitability of the neurons, the heterogeneity in the population, and the coupling strength (which can be excitatory or inhibitory). We find that the network typically tends toward the two macroscopic equilibrium states when the neuron's intrinsic dynamics and the network interactions reinforce one another. In contrast, the limit cycle state, bifurcations, and multistability tend to occur when there is competition among these network features. Finally, we show that our results are exhibited by finite network realizations of reasonable size.

scholarly journals Regular Traveling Waves in a One-Dimensional Network of Theta Neurons

2002 ◽  
Vol 62 (4) ◽  
pp. 1197-1221 ◽  
Author(s):  
Bard Ermentrout ◽  
Jonathan Rubin ◽  
Remus Osan
Keyword(s):  
Traveling Waves ◽  
One Dimensional ◽  
Dimensional Network ◽  
Theta Neurons

Coherence Resonance in Coupled Theta Neurons

2007 ◽  
Vol 50 (91) ◽  
pp. 219 ◽  
Author(s):  
Woochang Woochang ◽  
Sang-Yoon Sang-Yoon ◽  
Sunae Sunae
Keyword(s):  
Coherence Resonance ◽  
Theta Neurons

scholarly journals A Density Model for a Population of Theta Neurons

2014 ◽  
Vol 4 (1) ◽  
pp. 2 ◽  
Author(s):  
Grégory Dumont ◽  
Jacques Henry ◽  
Carmen Tarniceriu
Keyword(s):  
Density Model ◽  
Theta Neurons
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