马知恩. 种群生态学的数学建模与研究[M]. 合肥: 安徽教育出版社, 1996.
CAI Y L, KANG Y, BANERJEE M, et al. Complex Dynamics of a Host-Parasite Model with both Horizontal and Vertical Transmissions in a Spatial Heterogeneous Environment[J]. Nonlinear Analysis: Real World Applications, 2018, 40: 444-465. doi: 10.1016/j.nonrwa.2017.10.001
CAI Y L, LIAN X Z, PENG Z H, et al. Spatiotemporal Transmission Dynamics for Influenza Disease in a Heterogenous Environment[J]. Nonlinear Analysis: Real World Applications, 2019, 46: 178-194. doi: 10.1016/j.nonrwa.2018.09.006
伏升茂, 孙姣姣. 带强Allee效应的Rosenzweig-MacArthur捕食者-食饵模型的Hopf分支[J]. 西北师范大学学报(自然科学版), 2019, 55(1): 1-7.
LESLIE P H. Some Further Notes on the Use of Matrices in Population Mathematics[J]. Biometrika, 1948, 35(3-4): 213-245. doi: 10.1093/biomet/35.3-4.213
LESLIE P H. A Stochastic Model for Studying the Properties of Certain Biological Systems by Numerical Methods[J]. Biometrika, 1958, 45(1-2): 16-31. doi: 10.1093/biomet/45.1-2.16
PIELOU E C. Mathematical Ecology[M]. New York: John Wiley&Sons, 1977.
KOROBEINIKOV A. A Lyapunov Function for Leslie-Gower Predator-Prey Models[J]. Applied Mathematics Letters, 2001, 14(6): 697-699. doi: 10.1016/S0893-9659(01)80029-X
CREEL S, CHRISTIANSON D. Relationships between Direct Predation and Risk Effects[J]. Trends in Ecology & Evolution, 2008, 23(4): 194-201.
CRESSWELL W. Predation inBird Populations[J]. Journal of Ornithology, 2011, 152(1): 251-263. doi: 10.1007/s10336-010-0638-1
LIMA S L. Nonlethal Effects in the Ecology of Predator-Prey Interactions[J]. BioScience, 1998, 48(1): 25-34. doi: 10.2307/1313225
LIMA S L. Predators and the Breeding Bird: Behavioral and Reproductive Flexibility under the Risk of Predation[J]. Biological Reviews of the Cambridge Philosophical Society, 2009, 84(3): 485-513. doi: 10.1111/j.1469-185X.2009.00085.x
ZANETTE L Y, WHITE A F, ALLEN M C, et al. Perceived Predation Risk Reduces the Number of Offspring Songbirds Produce Per Year[J]. Science, 2011, 334(6061): 1398-1401. doi: 10.1126/science.1210908
WANG X Y, ZANETTE L, ZOU X F. Modelling the Fear Effect in Predator-Prey Interactions[J]. Journal of Mathematical Biology, 2016, 73(5): 1179-1204. doi: 10.1007/s00285-016-0989-1
WANG X Y, ZOU X F. Modeling the Fear Effect in Predator-Prey Interactions with Adaptive Avoidance of Predators[J]. Bulletin of Mathematical Biology, 2017, 79(6): 1325-1359. doi: 10.1007/s11538-017-0287-0
WANG J, CAI Y L, FU S M, et al. The Effect of the Fear Factor on the Dynamics of a Predator-Prey Model Incorporating the Prey Refuge[J]. Chaos, 2019, 29(8): 083109. doi: 10.1063/1.5111121
ZHANG H S, CAI Y L, FU S M, et al. Impact of the Fear Effect in a Prey-Predator Model Incorporating a Prey Refuge[J]. Applied Mathematics and Computation, 2019, 356: 328-337. doi: 10.1016/j.amc.2019.03.034
QIAO T, CAI Y L, FU S M, et al. Stability and Hopf Bifurcation in a Predator-Prey Model with the Cost of Anti-Predator Behaviors[J]. International Journal of Bifurcation and Chaos, 2019, 29(13): 1950185. doi: 10.1142/S0218127419501852