We consider the problem of reconstructing chaotic attractors from spike trains produced by model neurons. We nd that the period/parameter plot, which displays the dependence of the oscillation frequency of the spiking model on the input level, is a useful device for determining the success of reconstruction. A new three-dimensional version of Fitzhugh-Nagumo spiking dynamics is investigated alo...

We explore an embryonic heart model that couples electrophysiology and muscle-force generation to flow induced using a 2D fluid-structure interaction framework based on the immersed boundary method. The propagation of action potentials are coupled to muscular contraction and hence the overall pumping dynamics. In comparison to previous models, the electro-dynamical model does not use prescribed...

In this paper, we present a study of some high-order compact difference schemes for solving the Fitzhugh-Nagumo equations governed by two coupled time-dependent nonlinear reaction diffusion equations in two variables. Solving the Fitzhugh-Nagumo equations is quite challenging, since the equations involve spatial and temporal dynamics in two different scales and the solutions exhibit shock-like ...

Current induced oscillations of a space clamped neuron action potential demonstrates a bifurcation scenario originally encapsulated by the four dimensional Hodgkin-Huxley equations. These oscillations were subsequently described by the two dimensional FitzHugh-Nagumo Equations in close agreement with the HodgkinHuxley theory. It is shown that the FitzHugh-Nagumo equations can to close approxima...

In this study, we have done our simulation in two section. In the first step, we simulated the Hodgkin Huxley equations by MATLAB software and obtained the action potential waveform. In the second step, 3D simulation of FitzHugh Nagumo model in order to action potential generation and propagation in squid giant axon have been explored. Simulation of this section has been performed by using the ...

The dynamics of many systems from physics, economics, chemistry, and biology can be modelled through polynomial functions. In this paper, we provide a computational means to find positively invariant sets dynamical by using semidefinite programming solve sum-of-squares (SOS) programmes. With the emergence SOS programmes, it is possible efficiently search for Lyapunov functions that guarantee st...