
Mathematical Biosciences and Engineering, 2020, 17(4): 32743293. doi: 10.3934/mbe.2020187.
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Coexistence and extinction in a databased ratiodependent model of an insect community
1 School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287, USA
2 School of Mathematics and Statistics, Southwest University, Chongqing 400715, P.R. China
Received: , Accepted: , Published:
Keywords: coexistence; extinction; competition; stability; Predatorprey; Hopf bifurcation
Citation: Yang Kuang, Kaifa Wang. Coexistence and extinction in a databased ratiodependent model of an insect community. Mathematical Biosciences and Engineering, 2020, 17(4): 32743293. doi: 10.3934/mbe.2020187
References:
 1. H. I. Freedman, Deterministic Mathematical Models in Population Ecology, Marcel Dekker, Inc., New York, (1980).
 2. G. Hardin, The competitive exclusion principle, Science, 131 (1960), 12921297.
 3. G. F. Gause, The Struggle For Existence, Baltimore, Williams & Wilkins, (1934).
 4. Y. Kuang, H. I. Freedman, Uniqueness of limit cycles in Gausetype models of predatorprey systems, Math. Biosci., 88 (1988), 6784.
 5. F. J. F. van Veen, P. D. van Holland, H. C. J. Godfray, Stable coexistence in insect communities due to density and traitmediated indirect effects, Ecology, 86 (2005), 31823189.
 6. S. B. Hsu, T. W. Hwang, Y. Kuang, Rich dynamics of a ratiodependent one prey two predator model, J. Math. Biol., 43 (2001), 377396.
 7. S. B. Hsu, T. W. Hwang, Y. Kuang, A ratiodependent food chain model and its applications to biological control, Math. Biosci., 181 (2003), 5583.
 8. Y. Kuang, E. Beretta, Global qualitative analysis of a ratiodependent predatorprey system, J. Math. Biol., 36 (1998), 389406.
 9. S. B. Hsu, T. W. Hwang, Y. Kuang, Global analysis of the MichaelisMententype ratiodependent predatorprey system, J. Math. Biol., 42 (2001), 489506.
 10. T. W. Hwang, Y. Kuang, Deterministic extinction effect of parasites on host populations, J. Math. Biol., 46 (2003), 1730.
 11. T. W. Hwang, Y. Kuang, Host extinction dynamics in a simple parasitehost interaction model, Math. Biosci. Eng., 2 (2005), 743751.
 12. P. Waltman, A Second Course in Elementary Differential Equations, Reprinted, Dover Publications, (2004).
 13. E. Beretta, Y. Kuang, Modeling and analysis of a marine bacteriophage infection, Math. Biosci., 149 (1998), 5776.
 14. Z. E. Ma, Mathematical modeling and research of population ecology, Hefei: Anhui Education Press, (1996).
 15. Y. Kuang, J. D. Nagy, S. E. Eikenberry, Introduction to mathematical oncology, Chapman and HallCRC, (2016).
 16. W. M. Liu, Criterion of Hopf bifurcations without using eigenvalues, J. Math. Anal. Appl., 182 (1994), 250256.
 17. S. Hews, S. Eikenberry, J. D. Nagy, Y. Kuang, Rich dynamics of a hepatitis B viral infection model with logistic hepatocyte growth, J. Math. Biol., 60 (2010), 573590.
 18. H. R. Thieme, Mathematics in population biology, Princeton, (2003).
 19. E. Beretta, Y. Kuang, Modeling and analysis of a marine bacteriophage infection with latency period, Nonlinear Anal. RWA, 2 (2001), 3574.
 20. E. Beretta, Y. Kuang, Geometric stability switch criteria in delay differential systems with delay dependent parameters, SIAM J. Math. Anal., 33 (2002), 11441165.
 21. S. A. Gourley, Y. Kuang, A stage structured predatorprey model and its dependence on maturation delay and death rate, J. Math. Biol., 49 (2004), 188200.
 22. Y. Kuang, Delay differential equations with applications in population dynamics, Academic Press, (1993).
 23. E. Beretta, Y. Kuang, Global analyses in some delayed ratiodependent predatorprey systems, Nonlinear Anal. TMA, 32 (1998), 381408.
 24. Y. Kuang, W. Fagan, I. Loladze, Biodiversity, habitat area, resource growth rate and interference competition, Bull. Math. Biol., 65 (2003), 497518.
 25. R. Sterner, J. J. Elser, Ecological Stoichiometry, Princeton University Press, Princeton, NJ, (2002).
 26. I. Loladze, Y. Kuang, J. J. Elser, Stoichiometry in producergrazer systems: linking energy flow and element cycling, Bull. Math. Biol., 62 (2000), 11371162.
 27. I. Loladze, Y. Kuang, J. J. Elser, W. F. Fagan, Coexistence of two predators on one prey mediated by stoichiometry, Theor. Popul. Biol., 65 (2004), 115.
 28. X. Yang,X. Li, H. Wang, Y. Kuang, Stability and bifurcation in a stoichiometric producergrazer model with knife edge, SIAM J. Appl. Dyn. Syst., 15 (2016), 20512077.
 29. M. Chen, M. Fan, Y. Kuang, Global dynamics in a stoichiometric food chain model with two limiting nutrients, Math. Biosci., 289 (2017), 919.
 30. J. J. Elser, I. Loladze, A. L. Peace, Y. Kuang, Lotka reloaded: Modeling trophic interactions under stoichiometric constraints, Ecol. Model., 245 (2012), 311.
 31. A. Peace, H. Wang, Y. Kuang, Dynamics of a producergrazer model incorporating the effects of excess foodnutrient content on grazer's growth, Bull. Math. Biol., 76 (2014), 21752197.
 32. J. J. Elser, Y. Kuang, Ecological stoichiometry. In: Hastings, A., Gross, L. (eds.), Encyclopedia of Theoretical Ecology, University of California Press, (2012), 718722.
 33. D. O. Hessen, J. J. Elser, R. W. Sterner, J. Urabe, Ecological stoichiometry: An elementary approach using basic principles, Limnol. Oceanogr., 58 (2013), 22192236.
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