| Abstract: |
| Dilemmas involving trade-offs between acquiring food and avoiding threats are unavoidable in animals` daily lives. To enhance survival, they must continually adjust their movement in response to environmental cues, while internal hunger levels also strongly influence their decision-making processes. In this study, we develop a general coupled PDE--ODE model that integrates movement strategies driven by internal hunger dynamics. Even in the same environment, different species may prioritize different types of information. We investigate how various cognitive movement strategies affect species` survival outcomes in simplified food--threat dilemmas. Specifically, we compare five commonly observed strategies based on local gradients, regional maxima, global maxima, regional aggregate gradients, and global aggregate gradients. We prove the well-posedness of the model, in which a general function of the ODE variable appears in the taxis sensitivity function in the PDE equation, and we conduct a stability analysis around arbitrary equilibria. These results are then used to determine survival and extinction conditions under each strategy. Numerical simulations show that the effectiveness of movement strategies strongly depends on environmental context. The global-maximum strategy yields the greatest survival with minimal foraging and threat-avoidance effort in a simple dilemma, while in more complex multimodal environments, local strategies produce the highest population survival rate. |
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