BERRYMAN A A.The orgins and evolution of predator-prey theory[J].Ecology,1992,73(5):1530-1535．

FELLER W.On the logistic law of growth and its empirical verifications in biology[J].Acta Biotheoretica,1940,5(2):51-66．

BICK C S,LEE I,COOTE T,et al.Millimeter-sized smart sensors reveal that a solar refuge protects tree snail Partula hyalina from extirpation[J].Communications Biology,2021,4:744．

GAO S J,CHEN L S.The effect of seasonal harvesting on a single-species discrete population model with stage structure and birth pulses[J].Chaos,Solitons&Fractals,2005,24(4):1013-1023．

马兆芝，吴玉敏，陈凤德，等．捕食者的密度制约和食饵避难所对Lotka-Volterra捕食-食饵模型动力学行为影响的研究[J]．福州大学学报(自然科学版)，2012,40(6):699-703.MA Z Z,WU Y M,CHEN F D,et al.The influence of predator’s density dependence and prey refuge on the Lotka-Volterra predator-prey model[J].Journal of Fuzhou University(Natural Science Edition),2012,40(6):699-703.(in Chinese)

RODRIGUEZ L Q,GORDILLO L F.Density-dependent diffusion and refuge in a spatial Rosenzweig-Mac Arthur model:Stability results[J].Journal of Mathematical Analysis and Applications,2022,512(2):126174．

TENG Z D.On the non-autonomous Lotka-Volterra N-species competing systems[J].Applied Mathematics and Computation,2000,114(2/3):175-185．

FU S M,ZHANG H S.Effect of hunting cooperation on the dynamic behavior for a diffusive Holling type II predator-prey model[J].Communications in Nonlinear Science and Numerical Simulation,2021,99:105807．

HU Z Y,TENG Z D,ZHANG L.Stability and bifurcation analysis of a discrete predator-prey model with nonmonotonic functional response[J].Nonlinear Analysis:Real World Applications,2011,12(4):2356-2377．

程利芳．几类非线性动力系统的分岔与聚合行为研究[D]．北京：北京交通大学，2018.CHENG L F.Researchon bifurcation and collective behavior for several classes of nonlinear dynamical systems[D].Beijing:Beijing Jiaotong University,2018.(in Chinese)

KHAN A Q,BUKHARI S A H,ALMATRAFI M B.Global dynamics,Neimark-Sacker bifurcation and hybrid control in a Leslie’s prey-predator model[J].Alexandria Engineering Journal,2022,61(12):11391-11404．

KAR T K.Stability analysis of a prey-predator model incorporating a prey refuge[J].Communications in Nonlinear Science and Numerical Simulation,2005,10(6):681-691．

HOLLING C S.The functional response of predators to prey density and its role in mimicry and population regulation[J].Memoirs of the Entomological Society of Canada,1965,97(S45):5-60．

KUZNETSOV Y A.Elements of applied bifurcation theory[M].New York:Springer,1995．

GUCKENHEIMER J,HOLMES P.Nonlinear oscillations,dynamical systems,and bifurcations of vector fields[M].New York:Springer,1983.