Pattern Formation and analysis of reaction–diffusion ratio-dependent prey–predator model with harvesting in predator

A significant degree of complexity to the conventional ecological dynamic is added by studying prey–predator models with harvesting predators. The primary focus of classical models is the link between prey and predator populations, emphasizing their fundamental relationships and biological roles. A complex interaction between biological processes is shown when predator harvesting is combined with prey–predator models. This presents both opportunities and challenges for sustainable resource management. These models help the community to understand how much one can harvest without wiping out the predators or disturbing the balance of the ecosystem. In this study, spatially extended reaction–diffusion prey–predator dynamics with harvesting in predator is analyzed. The unconditionally positivity preserving scheme is applied for the numerical results. Pattern formation in the spatially extended system is also obtained. Various types of patterns like spots, stripes, and holes are observed by using extensive numerical simulations with various parameters. The numerical technique is unconditionally stable, dynamically consistent with the underlying model, preserves the positivity, has bounded behavior, and preserves the all true properties of the continuous model. The underlying model has two equilibrium points and both are successfully obtained with positive behavior for the whole domain. All the theoretical results are verified through the numerical simulations.