西北师范大学学报（自然科学版）2025，Vol.61Issue(5)：122-131,10.DOI:10.16783/j.cnki.nwnuz.2025.05.014
一类具有恐惧效应和线性收获项的捕食模型的动力学行为分析
Dynamical behavioural analysis for a class of predation models with fear effects and linear harvesting terms
摘要
Abstract
This study systematically investigated the dynamical properties for a predator-prey model with fear effects and linear harvesting terms through theoretical analysis and numerical simulations.Utilizing differential inequalities,the boundedness and persistence of solutions are proved,which can ensure biological plausibility of the model.The existence and stability of equilibrium points are thoroughly analyzed,and the global asymptotic stability at the positive equilibrium is rigorously verified via Dulac's criterion.Furthermore,by employing center manifold theorem and normal form theory,the critical conditions of Hopf bifurcation and stability criteria for periodic solutions are given.Numerical simulations validate the effectiveness of theoretical findings,while parameter sensitivity analysis elucidates the regulatory mechanisms of key parameters on system dynamics.关键词
恐惧效应/线性收获项/稳定性/Dulac函数/Hopf分岔Key words
fear effect/linear harvesting term/stability/Dulac function/Hopf bifurcation分类
数理科学引用本文复制引用
高鑫,冯孝周,李畅通..一类具有恐惧效应和线性收获项的捕食模型的动力学行为分析[J].西北师范大学学报（自然科学版）,2025,61(5):122-131,10.基金项目
国家自然科学基金资助项目(12326417) （12326417）
国家外专局项目(G2023041033L) （G2023041033L）
陕西省自然科学基金资助项目(2023ybgy016,2023wgzjzd08,2024jcybms072) （2023ybgy016,2023wgzjzd08,2024jcybms072）
陕西省教育厅科学研究项目(23JSY044) （23JSY044）
陕西省教学改革项目(23BY078) （23BY078）
西安工业大学研究生创新重点项目(XAGDYJ220106) （XAGDYJ220106）
