[1] H.R. Akcakaya, R. Arditi, L.R. Ginzburg, Ratio-dependent predation: An abstraction that works,
Ecology 76 (1995) 995-1004.
[2] W.C. Allee, Animal aggregations, The Quarterly Review of Biology 2 (1927) 367–398.
[3] W.C. Allee, E.S. Bowen, Studies in animal aggregations: Mass protection against colloidal silver
among goldfishes, Journal of Experimental Zoology 61 (1932) 185–207.
[4] R. Arditi, L.R. Ginzburg, Coupling in predator-prey dynamics: ratio-dependence, J. Theor. Biol.
139 (1989) 311–326.
[5] R. Arditi, L.R. Ginzburg, H.R. Akcakaya, Variation in plankton densities among lakes: A case for
ratio-dependent Predation Models, The American Naturalist 138 (1991) 1287-1296.
[6] E.A. Barbaˇsin, N.N. Krasovski˘ı, On stability of motion in the large, Doklady Akad. Nauk SSSR
(N.S.) 86 (1952) 453–456 (in Russian).
[7] C. Cosner, D.L. DeAngelis, J.S. Ault, D.B. Olsen, Effects of spatial grouping on the functional
response of predators, Theor. Pop. Biol. 56 (1999) 65–75.
[8] I. Bashkirtseva, L. Ryashko, Noise-induced shifts in the population model with a weak Allee effect,
Phys. A 491 (2018) 28–36.
[9] I. Bashkirtseva, T. Perevalova, Analysis of stochastic bifurcations in the eco-epidemiological oscil-
latory model with weak Allee effect, Internat. J. Bifur. Chaos Appl. Sci. Engrg. 32 (2022) Paper No.
2250124, 14.
[10] R. Benazic, T´opicos de Ecuaciones Diferenciales Ordinarias, UNI, Per´u, 2007.
[11] L. Berec, E. Angulo, F. Courchamp, Multiple Allee effects and population management, Trends in
Ecology & Evolution 22 (2006) 185–191.
[12] F. Brauer, C. Castillo-Chavez, Mathematical Models in Population Biology and Epidemiology,
Texts in Applied Mathematics, Springer, New Yor, 2012.
[13] G. Cardano, Ars Magna or the Rules of Algebra, Dover Publications, Inc., New York, 1993.
[14] C. Chicone, Ordinary Differential Equations with Applications, Springer, New York, 2006.
[15] F. Courchamp, L. Bereck, J. Gascoigne, Allee Effects in Ecology and Conservation, Oxford Uni-
versity Press, 2008.
[16] C. Egami, Positive periodic solutions of nonautonomous delay competitive systems with weak Allee
effect, Nonlinear Anal. Real World Appl. 10 (2009) 494–505.
[17] V. Fern´andez-Arhex, J.C. Corley, La respuesta funcional: una revisi´on y gu´ıa experimental,
Ecolog´ıa austral 14 (2004) 83–93.
[18] J.D. Ferreira, C.A.T. Salazar, P.C.C. Tabares, Weak Allee effect in a predator-prey model involving
memory with a hump, Nonlinear Anal. Real World Appl. 14 (2013) 536–548.
[19] E. Gonz´alez-Olivares, A. Rojas-Palma, Colaboraci´on entre depredadores y efecto Allee d´ebil en las
presas. Consecuencias sobre la din´amica de un modelo de depredaci´on, Selecciones Matem´aticas
9 (2022) 173–183.
[20] A.P. Gutierrez, Physiological basis of ratio-dependent predator-prey theory: The metabolic pool
model as a paradigm., Ecology 73 (1992) 1552-1563.
[21] L. Hanski, The functional response of predators: worries about scale, Trends. Ecol. Evol. 6 (1991)
141–142.
[22] R.A. Horn and C.R. Johnson, Matrix analysis, Cambridge University Press, 2013.
[23] Sze-Bi Hsu, Ordinary Differential Equations with Applications, World Scientific Publishing Co.
Pte. Ltd., Hackensack, NJ, 2013.
[24] J. P´erez–N´u˜nez, An´alisis y simulaci´on de un modelo matem´atico glucosa-insulina en personas con
diabetes tipo I, Ph. D. Thesis, UNMSM, Lima, Per´u, 2017.
[25] J. P´erez–N´u˜nez et al., A mathematical model the transmission dynamics of tuberculosis with exoge-
nous reinfection in the infection-free state, Int. J. Appl. Eng. Technol. 4 (2022) 38–45.
[26] X. Jia, K. Huang, C. Li, Bifurcation analysis of a modified Leslie-Gower predator-prey system,
Internat. J. Bifur. Chaos Appl. Sci. Engrg. 33 (2023) Paper No. 2350024, 24.
[27] A. Kramer, L. Berec, J.M. Drake, Allee effects in ecology and evolution, J. Anim. Ecol. 87 (2018)
7–10.
[28] J.P. LaSalle, Some extensions of liapunov’s second method, IRE Transactions on Circuit Theory
CT-7 (1960) 520–527.
[29] O. Lazaar, M. Serhani, Stability and optimal control of a prey-predator model with prey refuge and
prey infection, Int. J. Dyn. Control 11 (2023) 1934–1951.
[30] P.H. Leslie, Some further notes on the use of matrices in population mathematics, Biometrika 35
(1948) 213–245.
[31] C. Liang, H.F. Huo, H. Xiang, Modelling mosquito population suppression based on competition
system with strong and weak Allee effect, Math. Biosci. Eng. 21 (2024) 5227–5249.
[32] M. Liermann, R. Hilborn, Depensation: evidence, models and implications, Fish and Fisheries 2
(2001) 33–58.
[33] R. Lin, S. Liu, X. Lai, Bifurcations of a predator-prey system with weak Allee effects, J. Korean
Math. Soc. 50 (2013) 695–713.
[34] T. Liu, L. Chen, F. Chen, Z. Li, Dynamics of a Leslie-Gower model with weak Allee effect on
prey and fear effect on predator, Internat. J. Bifur. Chaos Appl. Sci. Engrg. 33 (2023) Paper No.
2350008, 19.
[35] A.J. Lotka, Elements of Physical Biology, Williams & Wilkins, Baltimore: Waverly, 1925.
[36] D. Luo, Q. Wang, Global dynamics of a Beddington-DeAngelis amensalism system with weak Allee
effect on the first species, J. Appl. Math. Comput. 68 (2022) 655–680.
[37] T. Ma, X. Meng, Global stability analysis and Hopf bifurcation due to memory delay in a novel
memory-based diffusion three-species food chain system with weak Allee effect, Math. Methods
Appl. Sci. 47 (2024) 6079–6096.
[38] V. Madhusudanan, S. Vijaya, Dynamical Behaviour in Two Prey-Predator System with Persistence,
Bull. Math. Anal. Appl. 16 (2016) 20–37.
[39] T.R. Malthus, An Essay on the Principle of Population, Penguin Classics, London, 1798.
[40] R.M. May, Stability and Complexity in Model Ecosystems, Princeton university press, 2001.
[41] O. Osuna, G. Villase˜nor, On the Dulac functions, Qual. Theory Dyn. Syst. 10 (2011) 43–49.
[42] O. Osuna, G. Villase˜nor, Some properties theDulac functions set, Electron. J. Qual. Theory Differ.
Equ. 2011 (2011) No. 72, 8.
[43] O. Osuna, C. Vargas-De-Le´on, Construction of Dulac functions for mathematical models in popu-
lation biology, Int. J. Biomath. 8 (2015) 1550035, 20.
[44] N.P. Romero, C.U. Fern´andez, Mathematical model of a predator-prey food chain: plankton-
anchovy,Rev. Mat. 29 (2022) 69–103.
[45] M. Romero–Ordo˜nez and J. P´erez–N´u˜nez and L. V´asquez–Serpa, An´alisis cualitativo y simu-
laciones de un modelo depredador–presa tipo May–Holling–Tanner r´azon–dependiente con una
fuente alternativa de alimento para el depredador, Sel. Mat. 9 (2022) 196–209.
[46] K. Sarkar, S. Khajanchi, P.C. Mali, A delayed eco-epidemiological model with weak Allee effect
and disease in prey, Internat. J. Bifur. Chaos Appl. Sci. Eng. 32 (2022) Paper No. 2250122, 26.
[47] S.K. Sasmal, J. Chattopadhyay, An eco-epidemiological system with infected prey and predator
subject to the weak Allee effect, Math. Biosci. 246 (2013) 260–271.
[48] S. Sastry, Nonlinear Systems, Springer-Verlag, New York, 1999.
[49] S. Sharma, G.P. Samanta, A ratio-dependent predator-prey model with Allee effect and disease in
prey, J. Appl. Math. Comput. 47 (2015) 345–364.
[50] J.J. Slotine and W. Li, Applied Nonlinear Control, Prentice-Hall, 1991.
[51] J. Sotomayor, Lic¸ ˜oes de Equac¸ ˜oes Diferenciais Ordin´arias, Instituto de Matem´atica Pura e Apli-
cada, Rio de Janeiro, 1979.
[52] P.A. Stephens, W.J. Sutherland, R.P. Freckleton, What is the Allee effect?, Oikos 87 (1999) 185–
190.
[53] P.C. Tabares, J.D. Ferreira, V. Rao, Weak Allee effect in a predator-prey system involving distributed
delays, Comput. Appl. Math. 30 (2011) 675–699.
[54] P. Turchin, Complex Population Dynamics: A Theoretical/Empirical Synthesis, Monographs in
Population Biology, Princeton University Press, Princeton, NJ, 2003.
[55] P.-F. Verhulst, Notice sur la loi que la population suit dans son accroissement, Correspondence
mathematique et physique 10 (1838) 113–129.
[56] S. Valenzuela-Figueroa, E. Gonz´alez-Olivares, A. Rojas-Palma, Influence of the weak Allee effect
on prey in a Leslie-Gower type predation model with sigmoid functional response, Rev. Mat. 29
(2022) 105–138.
[57] V. Volterra, Fluctuations in the abundance of a species considered mathematically, Nature 118
(1926) 558–560.
[58] M.H. Wang, M. Kot, Speeds of invasion in a model with strong or weak Allee effects, Math. Biosci.
171 (2001) 83–97.
[59] Y. Wang, J. Shi, Persistence and extinction of population in reaction-diffusion-advection model with
weak Allee effect growth, SIAM J. Appl. Math. 79 (2019) 1293–1313.
[60] W. Wu, Y. Ye, Existence and stability of almost periodic solutions of nonautonomous competitive
systems with weak Allee effect and delays, Commun. Nonlinear Sci. Numer. Simul. 14 (2009) 3993–
4002.
[61] L. Zhang, Y. Xu, G. Liao, Codimension-two bifurcations and bifurcation controls in a discrete
biological system with weak Allee effect, Internat. J. Bifur. Chaos Appl. Sci. Eng. 32 (2022) Paper
No. 2250036, 27.
[62] Q. Yang, X. Zhang, D. Jiang, M. Shao, Analysis of a stochastic predator-prey model with weak
Allee effect and Holling-(n + 1) functional response, Commun. Nonlinear Sci. Numer. Simul. 111
(2022) Paper No. 106454, 18 pp.
[63] L. Zhao, J. Shen, Relaxation oscillations in a slow-fast predator-prey model with weak Allee effect
and Holling-IV functional response, Commun. Nonlinear Sci. Numer. Simul. 112 (2022) Paper No.
106517, 19 pp.
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