In this paper, Adomian decomposition method (ADM) and Laplace decomposition method (LDM) used to obtain series solutions of Burgers-Huxley and Burgers-Fisher Equations. In ADM the algorithm is illustrated by studying an initial value problem and LDM is based on the application of Laplace transform to nonlinear partial differential equations. In ADM only few terms of the expansion are required t...

A new method for constructing first-passage-time probability density functions in the case of regular one-dimensional time homogeneous diffusion processes restricted between constant boundaries is proposed. Some diffusion processes of particular interest in neuronal modeling are considered and thoroughly discusses.

The e!ects of positive and negative correlation, c, between (N"100) random synaptic inputs (each "ring at 100 Hz) on the mean and coe$cient of variation (CV) of interspike interval (ISI) of the Hodgkin}Huxley model are examined, for di!erent IPSP/EPSP frequency ratios, r. Mean (ISI) and CV are approximately constant (30}40 ms, and 0.75, respectively) under independence for r3[0,1], unlike the l...

The Hodgkin-Huxley model, created in 1952, was one of the first models in computational neuroscience and remains the best studied neuronal model to date. Although many other models have a more detailed system description than the Hodgkin-Huxley model, it nonetheless gives an accurate account of various high-level neuronal behaviours. The fields of computational neuroscience and Systems Biology ...