We examine the efficiency of information processing in a balanced excitatory and inhibitory (E-I) network during the developmental critical period, when network plasticity is heightened. A multimodule network composed of E-I neurons was defined, and its dynamics were examined by regulating the balance between their activities. When adjusting E-I activity, both transitive chaotic synchronization with a high Lyapunov dimension and conventional chaos with a low Lyapunov dimension were found. In between, the edge of high-dimensional chaos was observed. To quantify the efficiency of information processing, we applied a short-term memory task in reservoir computing to the dynamics of our network. We found that memory capacity was maximized when optimal E-I balance was realized, underscoring both its vital role and vulnerability during critical periods of brain development.

In this study, I considered quantifying the strength of chaos in the population firing rate of a pulse-coupled neural network. In particular, I considered the dynamics where the population firing rate is chaotic and the firing of each neuron is stochastic. I calculated a time histogram of firings to show the variation in the population firing rate over time. To smooth this histogram, I used Bayesian adaptive regression splines and a gaussian filter. The nonlinear prediction method, based on reconstruction, was applied to a sequence of interpeak intervals in the smoothed time histogram of firings. I propose the use of the sum of nonlinearity as a quantifier of the strength of chaos. When applying this method to the firings of a pulse-coupled neural network, the sum of nonlinearity was seen to satisfy three properties for quantifying the strength of chaos. First, it can be calculated from spiking data alone. Second, it takes large values when applied to firings that are confirmed, theoretically or numerically, to be chaotic. Third, it reflects the strength of chaos of the original dynamics.

We propose a pulse neural network that exhibits chaotic pattern alternations among stored patterns as a model of multistable perception, which is reflected in phenomena such as binocular rivalry and perceptual ambiguity. When we regard the mixed state of patterns as a part of each pattern, the durations of the retrieved pattern obey unimodal distributions. We confirmed that no chaotic properties are observed in the time series of durations, consistent with the findings of previous psychological studies. Moreover, it is shown that our model also reproduces two properties of multistable perception that characterize the relationship between the contrast of inputs and the durations.

The dependence of the dynamics of pulse-coupled neural networks on random rewiring of excitatory and inhibitory connections is examined. When both excitatory and inhibitory connections are rewired, periodic synchronization emerges with a Hopf-like bifurcation and a subsequent period-doubling bifurcation; chaotic synchronization is also observed. When only excitatory connections are rewired, periodic synchronization emerges with a saddle node–like bifurcation, and chaotic synchronization is also observed. This result suggests that randomness in the system does not necessarily contaminate the system, and sometimes it even introduces rich dynamics to the system such as chaos.

The roles of inhibitory neurons in synchronous firing are examined in a network of excitatory and inhibitory neurons with Watts and Strogatz's rewiring. By examining the persistence of the synchronous firing that exists in the random network, it was found that there is a probability of rewiring at which a transition between the synchronous state and the asynchronous state takes place, and the dynamics of the inhibitory neurons play an important role in determining this probability.

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. When electrical synapses are introduced, 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.

To study the synchronized oscillations among distant neurons in the visual cortex, we analyzed the synchronization between two modules of pulse neural networks using the phase response function. It was found that the intermodule connections from excitatory to excitatory ensembles tend to stabilize the antiphase synchronization and that the intermodule connections from excitatory to inhibitory ensembles tend to stabilize the in-phase synchronization. It was also found that the intermodule synchronization was more noticeable when the inner-module synchronization was weak.

Synchronized firings in the networks of class 1 excitable neurons with excitatory and inhibitory connections are investigated, and their dependences on the forms of interactions are analyzed. As the forms of interactions, we treat the double exponential coupling and the interactions derived from it: pulse coupling, exponential coupling, and alpha coupling. It is found that the bifurcation structure of the networks depends mainly on the decay time of the synaptic interaction and the effect of the rise time is smaller than that of the decay time.