The boundedness and asymptotic behavior of solutions for a predator-prey system with prey-stage structure, prey-taxis and intra-species competition are investigated. To compare with the classical predator-prey system, one distinct characteristic of the system is the inclusion of a prey-stage structure, which divides the prey into two stages: immature and mature. Another characteristic is the intra-species competition on the immature prey and predator in the system. It is shown that our system possesses a globally bounded classical solution under the stronger intra-species competition on the predator. In particular, we demonstrate the stability of the extinction steady state and semi-coexistence steady state as well as coexistence steady state under the precise conditions on variable parameters.
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Wu et al. (2024) studied this question.
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