Rewiring-induced Synchronization and Chaos in Pulse-coupled Neural Networks




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Explanation of Applet

Firing of neurons On the 100x100 two-dimensional grid, an excitatory neuron (E) and an inhibitory neuron (I) are placed.
The firings of excitatory neurons and inhibitory neurons are shown by yellow dots and blue dots, respectively.
The firings of both neurons are shown by green dots.
The plane of the connection strength g between E&I ensembles and rewiring probability p By regulating the values of the connection strength g between E&I ensembles and the rewiring probability p, you can observe asynchronous firing (async.) and synchronous firing (sync.).
In this simulator, you can choose the dynamics from two asynchronous dynamics and two synchronous dynamics, which are periodic synchronization and chaotic synchronization, by clicking this (g,p) plane or by using the choice on upper right.
(JE,JI) Flows of the ensemble-averaged firing rates JE and JI for excitatory and inhibitory ensemble are shown in the (JE,JI) plane.

Asynchronous firing shows an equilibrium, and synchronous firing shows time-varying dynamics, such as a limit cycle and a chaotic attractor.
Temporal changes in JE(t) and JI(t) Temporal changes in JE(t) and JI(t) are shown.
Yellow and blue denote the excitatory and inhibitory ensemble, respectively.


In the previous simulations "Chaos in a Pulse Neural Network : Analysis of Synchronization with the Fokker-Planck Equation" and "Stochastic Synchrony of Chaos in a Pulse Neural Network with Electrical Synapses", the connection among neurons are global, namely, a neuron connects to the other neurons in the network. When the number of neurons is large, the global connection is equivalent to random connection.

However, the actual neurons have restrictions on the number and the distance of connections, so we must incorporate these properties into our model, in other words, we must incorporate spatial structures into our model. As for the models with spatial structures, in 1998, Watts and Strogatz proposed a model with probabilistic rewiring of connections. The Watts-Strogatz (WS) model is obtained by rewiring the connections of locally connected network with probability p. When p=0, WS model is a locally connected network, and when p=1, it becomes a random (or globally connected) network. We can obtain various network model by regulating a single parameter p.

Moreover, it is known that the WS model has so-called small-world properties when p is small (typically, 0.01<p<0.1), namely, "a small average shortest path length" and "a large clustering coefficient." Such properties are often observed in social networks, the Internet, gene networks, and so on.

With the simulator models we can examine the dynamics of the network composed of excitatory and inhibitory neurons that are arranged on a two-dimensional array with 100x100 grids. In each grid, both an excitatory neuron and an inhibitory neuron are placed, and there are E->E, E->I, I->E, and I->I connections. The probabilistic rewiring of connections is introduced to E->E, E->I, and I->E connections. Moreover, in the original paper, the network only with E->E and E->I connections are analyzed. The inter-ensemble connection strength g is common to E->I and I->E connections.

It was found that the firing of the network changes from asynchronous to synchronous at a critical p when p is increased from 0, which is observed in the (g,p) plane in the simulator. This critical p depends on the inter-ensemble connection strength g, and when g is small, the critical p also take small values, as small as the values in the small world region (0.01<p<0.1).

In this simulator, you can choose the dynamics from two asynchronous dynamics and two synchronous dynamics, which are periodic synchronization and chaotic synchronization, by clicking this (g,p) plane or by using the choice on upper right.

This page is based on the following paper.
<< Stochastic Synchrony of Chaos in a Pulse Neural Network with Electrical Synapses
^ Chaotic Pattern Transitions in Pulse Neural Networks >>

Introduction to Chaos and Nonlinear Dynamics