Contents 1. Introduction 5 1.1. Nonlinear behaviors, time scales, our approach 5 1.2. Electrical activity of cells 6 2. Revisiting the Hodgkin-Huxley equations 10 2.1. Background and formulation 10 2.2. Hodgkin-Huxley gating equations as idealized kinetic models 12 2.3. Dissection of the action potential 13 2.3.1. Current-voltage relations 13 2.3.2. Qualitative view of fast-slow dissection 15 2...

We consider the problem of state and parameter estimation for a class of nonlinear oscillators defined as a system of coupled nonlinear ordinary differential equations. Observable variables are limited to a few components of state vector and an input signal. This class of systems describes a set of canonic models governing the dynamics of evoked potential in neural membranes, including Hodgkin-...

Neuron encodes and transmits information through generating sequences of output spikes, which is a high energy-consuming process. The spike is initiated when membrane depolarization reaches a threshold voltage. In many neurons, threshold is dynamic and depends on the rate of membrane depolarization (dV/dt) preceding a spike. Identifying the metabolic energy involved in neural coding and their r...

Modelling of the neural networks plays its important role during the long lasting effort for better understanding the function of neural systems. Traditionally, the single components of the networks were some simple neuronal models of yes/no character and discrete time scale like the logical neuron of McCulloch and Pitts. However, during more recent period, the networks have became more realist...

The dynamical behaviour of the forced escape oscillator, which depends on the parameter values we considered, have been studied numerically using the techniques of phase portraits and Poincar'{e} sections. Also, we employed perturbation methods such as Lindstedt's method to obtain the frequency-amplitude relation of escape oscillator.