Stochastic Synchrony of Chaos in a Pulse-Coupled Neural Network with Both Chemical and Electrical Synapses Among Inhibitory Neurons

Abstract

The synchronous firing of neurons in a pulse coupled neural network composed of excitatory and inhibitory neurons is analyzed. The neurons are connected by both chemical synapses and electrical synapses among the inhibitory neurons. By introducing electrical synapses, periodically synchronized firing as well as chaotically synchronized firing is widely observed. Moreover, we find stochastic synchrony where the ensemble-averaged dynamics shows synchronization in the network but each neuron has a low firing rate and the firing of the neurons seems to be stochastic. Stochastic synchrony of chaos corresponding to a chaotic attractor is also found.

Roles of Inhibitory Neurons in Rewiring-Induced Synchronization in Pulse-Coupled Neural Networks

“…The parameters are set as g EE = g II ≡ g int and g EI = g IE ≡ g ext for simplicity. Kanamaru & Aihara (2008) analyzed the dependence of synchronization only on g EE , g II , g EI , or g IE in the global network that corresponds to our model with p = 1 and found that the synchronous firing exists only in some range of g EE , g II , g EI , and g IE . Moreover, the time constants of the internal dynamics and the synaptic transmission are set to τ E = 1, τ I = 0.5, κ E = 1, and κ I = 5.…”

“…where X = E or I, and δ ij is Kronecker's delta (Ermentrout, 1996;Izhikevich, 1999;Kanamaru & Aihara, 2008). Although the number of excitatory neurons in the cortex is much larger than that of inhibitory neurons, we set both numbers identical for simplicity.…”

“…In the following, the parameters are set to g gap = 0.10, g int = 5, g ext = 3.2, and D = 0.004 so that this network shows synchronous firing for p = 1 (Kanamaru & Aihara, 2008) because we wish to clarify whether the synchronous firing persists even for small p. In Figures 2 and 3, the firing of neurons in the E-rewiring network with p = 0.6 and p = 0.8 is shown, respectively. Figures 2A, 2C, 3A, and 3C show the firing rates J E and J I of the excitatory and inhibitory ensemble, which are defined as an average instantaneous firing rate of a neuron, namely,…”

“…Three values of the connection strength of the electrical synapses, g gap = 0, 0.1, and 0.3, both for the E-rewiring and the E, I-rewiring networks are investigated. Note that in the network with g gap = 0, p 0 does not exist for g ext > 3.6 because globally synchronous firing does not exist in this range (Kanamaru & Aihara, 2008). The number of data points for g ext < 2.5 is small because the data were insufficient for fitting A tanh(β(p − p 0 )) + δ to S(J E ; p) when p 0 is close to 0, and fitting becomes difficult due to the small magnitude of A.…”

“…In these networks, it was found that the forms of interactions play critical roles in the generation of synchrony, such as the rise and decay time of the post synaptic potential. On the other hand, in the case of the network of excitable neurons, each of which does not emit spikes without disturbance, it is known that the network composed of both excitatory and inhibitory neurons shows synchronous firing when the strength of the connections and the amount of disturbance are appropriately chosen (Brunel, 2000;Kanamaru & Sekine, 2003, 2005Kanamaru & Aihara, 2008). The connections of the network of the above theoretical models are either random or all-to-all, and the dependence of synchrony on the topology of the network has not been examined.…”