We investigate a nonautonomous predator–prey model system with a Crowley–Martin functional response. We perform rigorous mathematical analysis and obtain conditions for (a) global attractivity and permanence in the form of integrals which improve the traditional conditions obtained by using bounds of involved parameters; and (b) the existence of periodic solutions applying continuation theorem from coincidence degree theory which has stronger results than using Brouwer fixed point theorem. Our result also indicates that the global attractivity of periodic solution is positively affected by the predator's density dependent death rate. We employ partial rank correlation coefficient method to focus on how the output of the model system analysis is influenced by variations in a particular parameter disregarding the uncertainty over the remaining parameters. We discuss the relations between results (permanence and global attractivity) for autonomous and nonautonomous systems to get insights on the effects of time‐dependent parameters.

中文翻译：

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具有Crowley-Martin功能反应的捕食者与被捕食者模型：一项非自治研究

我们研究了具有克劳利-马丁功能响应的非自治捕食者-猎物模型系统。我们进行严格的数学分析，并获得以下条件：（a）整体形式的整体吸引性和永久性，这些条件通过使用相关参数的范围来改善传统条件；（b）符合度数理论应用连续定理的周期解的存在性，其结果比使用布劳威尔不动点定理的结果强。我们的结果还表明，周期解的全局吸引性受到捕食者依赖密度的死亡率的积极影响。我们采用偏秩相关系数方法来关注模型系统分析的输出如何受到特定参数变化的影响，而忽略其余参数的不确定性。我们讨论了自治系统和非自治系统的结果（永久性和全局吸引性）之间的关系，以了解时间相关参数的影响。