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 of ...

We consider an Allen-Cahn type equation of the form ut = ∆u + εf(x, t, u), where ε is a small parameter and f(x, t, u) = f(u) − εg(x, t, u) a bistable nonlinearity associated with a double-well potential whose well-depths can be slightly unbalanced. Given a rather general initial data u0 that is independent of ε, we perform a rigorous analysis of both the generation and the motion of interface....

For a scalar reaction-diffusion equation, traveling wave is special type of solution which as function time transforms higher energy equilibrium state to lower state. Thus such propagation can be viewed an invasion one by different one. Similar phenomena have been obtained for variety systems equations possessing gradient structure. Our main goal in this paper, study the following two questions...

The stochastic response of the FitzHugh-Nagumo model is addressed using a modified Van der Pol (VDP) equation with fractional-order derivative and Gaussian white noise excitation. Via generalized harmonic balance method, term related to fractional splitted into equivalent quasi-linear dissipative force restoring force, leading an VDP without derivative. The analytic...

Using a model system of FitzHugh-Nagumo type in the excitable regime, the similarity between synchronization of self-sustained and noise-induced oscillations is studied for the case of more than one main frequency in the spectrum. It is shown that this excitable system undergoes the same frequency lockings as a self-sustained quasiperiodic oscillator. The presence of noise-induced both stable a...

This work formulates a new approach to reduced modeling of parameterized, time-dependent partial differential equations (PDEs). The method employs Operator Inference, scientific machine learning framework combining data-driven and physics-based modeling. parametric structure the governing is embedded directly into reduced-order model, parameterized operators are learned via linear regression pr...

Using the FitzHugh-Nagumo equations to represent oscillatory electrical behavior of $\ensuremath{\beta}$-cells, we develop a coupled oscillator network model with cubic lattice topology, showing that emergence pacemakers or hubs in system can be viewed as natural consequence population diversity. The optimal hub nonhub ratio is determined by position diversity-induced resonance maximum for give...

We have studied the dynamical properties of finite N -unit FitzHugh-Nagumo (FN) ensembles subjected to additive and/or multiplicative noises, reformulating the augmented moment method (AMM) with the Fokker-Planck equation (FPE) method [H. Hasegawa, J. Phys. Soc. Jpn. 75, 033001 (2006)]. In the AMM, original 2N -dimensional stochastic equations are transformed to eight-dimensional deterministic ...