Stability and convergence analysis of Fourier pseudo-spectral method for FitzHugh-Nagumo model

Analysis of the Dynamical Properties of Discrete Predator‐Prey Systems with Fear Effects and Refuges

“…Discrete predator-prey systems can exhibit complex dynamical behavior, which has attracted many researchers to study them [3][4][5][6]. Zhang et al [7] studied the dynamics of a discrete FitzHugh-Nagumo model by applying central manifold and normal form analysis and demonstrated that the system is capable of undergoing Neimark-Sacker and fip bifurcations even in the absence of difusion. Li et al [8] obtained rich dynamic properties by building a space-time discrete model with periodic boundary conditions.…”

“…To validate the accuracy of the theoretical proof, numerical simulations are conducted in the following sections. When the parameters are taken as h � 0.168989, r � 0.2, K � 4.94, d � 0.8, c � 0.8, b � 0.01, e � 0.5, a � 0.5, m � 0.76, (7) is satisfed; see Figure 4.…”

Efficient numerical method for the Fitzhugh-Nagumo equations with Neumann boundary conditions

“…In the past few decades, many researchers have done for the numerical solution of the FN equations. Various numerical methods have been announced including the finite difference method [4][5][6], Haar wavelet method [7], finite element method [8][9], spectral method [2,[10][11][12] and so on [3]. Recently, Muhammad et al derived a stochastic explicit scheme to approximate the stochastic FN model.…”