The ideas and techniques developed in [12,3] are extended to a basic stage structured model. Each strategy consists of two stages: a Juvenile (L for larvae), and Adult (A). A general model of this basic stage structure is formulated as a dynamical system on the state space of finite signed measures.Nonnegativity, well-posedness and uniform eventual boundedness are established under biologically natural conditions on the rates. Similar to [12] we also have the unifying of discrete and continuous systems and the containment of the classic nonlinearities.
Citation: John Cleveland. Basic stage structure measure valued evolutionary game model[J]. Mathematical Biosciences and Engineering, 2015, 12(2): 291-310. doi: 10.3934/mbe.2015.12.291
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Abstract
The ideas and techniques developed in [12,3] are extended to a basic stage structured model. Each strategy consists of two stages: a Juvenile (L for larvae), and Adult (A). A general model of this basic stage structure is formulated as a dynamical system on the state space of finite signed measures.Nonnegativity, well-posedness and uniform eventual boundedness are established under biologically natural conditions on the rates. Similar to [12] we also have the unifying of discrete and continuous systems and the containment of the classic nonlinearities.
References
|
[1]
|
Discrete Contin. Dyn. Syst. Ser. B, 5 (2005), 917-928.
|
|
[2]
|
Math. Models Methods Appl. Sci., 9 (1999), 1379-1391.
|
|
[3]
|
submitted JDE.
|
|
[4]
|
Springer-Verlag, 1994.
|
|
[5]
|
The American Naturalist, 177 (2011), 397-409.
|
|
[6]
|
J. Math. Biol., 27 (1989), 179-190.
|
|
[7]
|
Ann. Rev. Ecol. Evol. Syst., 38 (2007), 403-435.
|
|
[8]
|
J. Math. Biol., 48 (2004), 135-159.
|
|
[9]
|
J. Math. Biol., 54 (2007), 489-511.
|
|
[10]
|
Theoretical Population Biology, 69 (2006), 297-321.
|
|
[11]
|
Cambridge University Press, Cambridge, 1994.
|
|
[12]
|
Nonlinear Anal. Real World Appl., 14 (2013), 785-797.
|
|
[13]
|
Math. Model. Nat. Phenom., 1 (2006), 65-82.
|
|
[14]
|
Integr. Equ. Oper. Theory, 63 (2009), 351-371.
|
|
[15]
|
Journal of mathematical biology, 63 (2011), 493-517.
|
|
[16]
|
Biology Direct, 1 (2006), 1-19.
|
|
[17]
|
PNAS, 54 (1965), 731-736.
|
|
[18]
|
Ecology, 63 (1982), 607-615.
|
|
[19]
|
Secaucus, New Jersey, Springer Verlag, 1983.
|
|
[20]
|
Belknap Press, 2006.
|
|
[21]
|
Frontiers in Mathematics series, Birkhauser, 2007.
|
|
[22]
|
Monatsh. Math., 165 (2012), 117-144.
|
|
[23]
|
Acta Appl. Math., 114 (2011), 1-14.
|
|
[24]
|
Nature, 246 (1973), 15-18.
|
|
[25]
|
Princeton University Press, 2003.
|
|
[26]
|
Math. Biosci., 180 (2002), 207-235.
|
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