Introduction The behavior of neurons has been modeled with circuit elements for a long time. Hodgkin and Huxley developed their theory of action potential generation through circuit elements with active variable conductances that generated the non-linear dynamics of the action potential. Luckily for Hodgkin and Huxley, the squid axon which they studied only contained two types of active channel...

There has been an increasing interest in analyzing neurophysiology from complex and chaotic systems viewpoint in recent years. For example, although the famous Hodgkin and Huxley model (Hodgkin and Huxley, 1952) has been the basis of almost all of the proposed models for neural firing, the Rose-Hindmarsh model (Hindmarsh and Rose, 1984) is known to be a more refined model because as it has the ...

The Hodgkin Huxley model of the biological neuron is numerically solved in Java, using both an Euler and a 4 order Runge Kutta method. The theory behind the Hodgkin Huxley model is described and the basic spikes are investigated using a graphical program developed by the authors. This is the first step in a long-term goal to develop a tool in Java to simulate neuron interactions on a larger sca...

Abstract In Chapter 6, we studied a simple version of the cable equation, where diffusion term was added to FitzHugh-Nagumo equations. this chapter, will revisit equation and go through derivation model. addition, consider numerical solution for neuronal axon with membrane dynamics modeled by Hodgkin-Huxley