Huxley equation is a core mathematical framework for modern biophysically based neural modeling. It is often useful to obtain a generalized solitary solution for fully understanding its physical meanings. There are many methods to solve the equation, but each method can only lead to a special solution. This paper suggests a relatively new method called the Exp-function method for this purpose. ...

We consider the problem of desynchronizing a network of synchronized, globally (all-to-all) coupled neurons using an input to a single neuron. This is done by applying the discrete time dynamic programming method to reduced phase models for neural populations. This technique numerically minimizes a certain cost function over the whole state space, and is applied to a Kuramoto model and a reduce...

We discuss the gain in signal-to-noise ratio (SNR) recently reported by Liu et al. [Phys. Rev. E 63, 051912 (2001)] in the Hodgkin-Huxley neuronal model. We show first that the possibility of signal-to-noise ratio enhancements can be checked by consideration of the statistical characteristics of switching between the system states, and we examine how the SNR depends on the shape of a periodic s...

In this study, we try to implant chaotic features into the learning algorithm of self-organizing map. We call this concept as Chaotic SOM (CHAOSOM). As a first step to realize CHAOSOM, we consider the case that learning rate and neighboring coefficient of SOM are refreshed by chaotic pulses generated by the Hodgkin-Huxley equation. We apply the CHAOSOM to solve a traveling salesman problem and ...