Numerical Simulations of Traveling and Stationary Wave Solutions Arising from Reaction-Diffusion Population Models with Delay and Nonlocality

摘要

AbstractThe present work aims to provide sufficient background and rationale required for a deeper understanding of wave solutions of reaction-diffusion (RD) population models with delay and nonlocality. Using a two-age-class modeling approach, a delayed nonlocal RD model is extended from a one-dimensional to n-dimensional unbounded domain. The extended model and its reduced forms are employed to investigate the wave dynamics of invasive species. The analytical methods for investigating the existence, uniqueness, stability and monotonicity of wave solutions of the model and its reduced forms are briefly surveyed. The accompanying examples and the numerical simulations of delayed nonlocal RD models provide the reader with a grasp of the possible impacts of delay and diffusion on the behavior of traveling and stationary waves solutions. Moreover, formation of traveling wavefronts and the convergence of model solutions to stationary fronts and pulses are numerically explored.]]>