(untitled) (Contemporary Mathematics, 2025)
The impact of climate change has become a very important topic and can have a direct impact on predator-prey interactions. Therefore, in this paper, we introduce a novel competitive predator-prey model under the negative effects of climate change due to its effects and importance. Based on their different properties, Holling type I and II functional responses are considered to be two different models for studying dynamic behaviors. Two approaches to the negative impacts of climate change are assumed: static and periodic changes. Firstly, models with negative climate change are taken as static changes. The existence, positivity, and boundedness of solutions are established. Local and global stability conditions are obtained for all feasible equilibrium points. The Hopf bifurcation is investigated, by taking climate change constants, as bifurcation parameters. Which shows that the model with Holling type I is globally stable whenever there exists an internal equilibrium point. However, the model with Holling type II contains two dynamics: stable and limit cycle dynamics. Uniform persistence is proved, and various extinction scenarios have been analytically yielded. In addition, numerical simulations are used to demonstrate and verify our theoretical findings. Negative climate impacts have a significant impact on system stability as well as on the coexistence and extinction of species. Secondly, models with negative climate change are considered periodic changes taking seasonality into account, which is considered tangible evidence of climate change. The dynamics of these effects are investigated numerically. Due to the existence of seasonality, the dynamics become more complex and different, as there are multiple cycles and chaos, which makes the systems more realistic for describing some environments due to the presence of some environmental impacts. The findings of this study show many undesirable scenarios for predator-prey interactions due to negative climate change. In light of these findings, many phenomena and changes due to negative climate change in ecosystems can be explained and predicted from an ecological point of view.