Dynamical Behavior of the linearized Version of the FitzHugh-Nagumo Neural Model
نویسندگان
چکیده
For a linearized version of the FitzHugh–Nagumo model, firing and resetting conditions are defined by analogy with the Integrate and Fire model. The dynamical behavior of the model, subject to periodic synaptic inputs, is investigated both theoretically and numerically, with particular emphasis on the synchronization properties. The study is then extended to a network of two synaptically coupled units.
منابع مشابه
Pattern Formation of the FitzHugh-Nagumo Model: Cellular Automata Approach
FitzHugh-Nagumo (FHN) model is a famous Reaction-Diffusion System which first introduced for the conduction of electrical impulses along a nerve fiber. This model is also considered as an abstract model for pattern formation. Here, we have used the Cellular Automata method to simulate the pattern formation of the FHN model. It is shown that the pattern of this model is very similar to those...
متن کاملAn improved pseudospectral approximation of generalized Burger-Huxley and Fitzhugh-Nagumo equations
In this research paper, an improved Chebyshev-Gauss-Lobatto pseudospectral approximation of nonlinear Burger-Huxley and Fitzhugh- Nagumo equations have been presented. The method employs chebyshev Gauss-Labatto points in time and space to obtain spectral accuracy. The mapping has introduced and transformed the initial-boundary value non-homogeneous problem to homogeneous problem. The main probl...
متن کاملA new reduced mathematical model to simulate the action potential in end plate of skeletal muscle fibers
Usually mathematicians use Hodgkin-Huxley model or FitzHug-Nagumo model to simulate action potentials of skeletal muscle fibers. These models are electrically excitable, but skeletal muscle fibers are stimulated chemically. To investigate skeletal muscle fibers we use a model with six ordinary differential equations. This dynamical system is sensitive to initial value of some variables so it is...
متن کاملRiccati-Based Feedback Control of the Monodomain Equations With the Fitzhugh-Nagumo Model
Feedback control for the monodomain equations is studied. The dynamics of interest are governed by a coupled PDE-ODE reaction diffusion system with non-monotone nonlinearity of FitzHugh-Nagumo type. A localized distributed control is used to locally stabilize the nonlinear system. This is achieved by a Riccati-based feedback law, determined by the linearized system. It is shown that the Riccati...
متن کاملA Comparative Study of the Hodgkin-huxley and Fitzhugh-nagumo Models of Neuron Pulse Propagation
The four-dimensional Hodgkin–Huxley equations are considered as the prototype for description of neural pulse propagation. Their mathematical complexity and sophistication prompted a simplified two-dimensional model, the FitzHugh–Nagumo equations, which display many of the former’s dynamical features. Numerical and mathematical analysis are employed to demonstrate that the FitzHugh–Nagumo equat...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- I. J. Bifurcation and Chaos
دوره 11 شماره
صفحات -
تاریخ انتشار 2001