Reaction-diffusion modeling of the spread of spruce budworm in boreal ecosystem

An Unconditionally Stable Positivity-Preserving Scheme for the One-Dimensional Fisher–Kolmogorov–Petrovsky–Piskunov Equation

“…Castillo and Gómez [21] used the local discontinuous Galerkin method with the symmetric Strang operator splitting scheme to solve Fisher-KPP. Kabir [22] considered a model with travelling wave solutions with a qualitatively similar structure to that observed in the Fisher-KPP equation and performed numerical simulations. McCue et al [23] studied exact sharp-fronted travelling wave solutions of the Fisher-KPP equation to the Fisher-Stefan-type moving boundary problem.…”

Stability Analysis of a Single-Species Markovian Jumping Ecosystem

“…Animal populations will inevitably spread because of climate, foraging and random walking. And hence the reaction-diffusion ecological models well simulate the real ecosystem, and ( [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]). Particularly, reaction-diffusion ecosystem were studied in [11][12][13][14][15][16][17][18][19][20][21].…”

“…And hence the reaction-diffusion ecological models well simulate the real ecosystem, and ( [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]). Particularly, reaction-diffusion ecosystem were studied in [11][12][13][14][15][16][17][18][19][20][21]. For example, in [12], a single-species Markovian jumping ecosystem with diffusion and delayed feedback under Dirichlet boundary value was investigated:…”

“…For example, freshwater fish do not enter the sea through rivers. Inspired by some ideas or methods of the related literature [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28]30], the author is to investigate the stability of a single-species Markovian jumping ecosystem with diffusion and delayed feedback under Neumann zero boundary value.…”