MR3241909
Masataka KUWAMURA
Masataka KUWAMURA
Stability of Coexisting Equilibrium of Prey-Predator Systems with Dormancy of Predators
Funkcialaj Ekvacioj. Serio Internacia
57
2014
339--350
http://fe.math.kobe-u.ac.jp/FE/FullPapers/57-2/57_339.pdf
http://www.ams.org/mathscinet-getitem?mr=MR3241909
In this paper, we study the stability of a coexistence equilibrium in a prey-predator system with dormancy of predators. The results suggest that dormancy of predators can stabilize the population dynamics of prey-predator systems if the switch to predators entering dormancy is very sharp or if both the hatching and mortality rates of dormant predators are sufficiently low.
Prey-predator system, Coexisting equilibrium, Dormancy.
34D20, 92D25.
57-339
2014
Stability of Coexisting Equilibrium of Prey-Predator Systems with Dormancy of Predators
Masataka KUWAMURA
Masataka KUWAMURA
1
Bazykin, A. D.
Nonlinear Dynamics of Interacting Populations
World Scientific Series on Nonlinear Science, Series A: Monographs and Treatises, 11, World Scientific Publishing Co., Inc., River Edge, NJ
1998
MR1635219
2
Begon, M.; Harper, J. L.; Townsend, C. R.
Ecology: Individuals, Populations, and Communities
3rd edition, Blackwell Publ.
1996
3
Bilinsky, L.; Hadeler, K. P.
Quiescence stabilizes predator-prey relations
J. Biol. Dyn.
3
2009
196-208
MR2574003
4
Doedel, E. J.; Champneys, A. R.; Fairgrieve, T. F.; Kuznetsov, Y. A.; Oldeman, B. E.; Paffenroth, R. C.; Sandstede, B.; Wang, X., AUTO 2000: Continuation and bifurcation software for ordinary differential equations (with HomCont), 2000
5
Gantmacher, F. R.
Applications of the Theory of Matrices
Interscience Publishers Inc., New York; Interscience Publishers Ltd., London
1959
MR0107648
6
Gyllström, M.; Hansson, L.-A.
Dormancy in freshwater zooplankton: Induction, termination and the importance of benthic-pelagic coupling
Aquat. Sci.
66
2004
274-295
7
Kuwamura, M.; Chiba, H.
Mixed-mode oscillations and chaos in a prey-predator system with dormancy of predators
Chaos
19
2009
043121, 10pp
MR2603669
8
Kuwamura, M.; Nakazawa, T.
Dormancy of predators dependent on the rate of variation in prey density
SIAM J. Appl. Math.
71
2011
169-179
MR2776832
9
Kuwamura, M.; Nakazawa, T.; Ogawa, T.
A minimum model of prey-predator system with dormancy of predators and the paradox of enrichment
J. Math. Biol.
58
2009
459-479
MR2470198
10
Nakazawa, T.; Kuwamura, M.; Yamamura, N.
Implications of resting eggs of zooplankton for the paradox of enrichment
Popul. Ecol.
53
2011
341-350
11
Rosenzweig, M. L.; MacArthur, R. H.
Graphical representation and stability conditions of predator-prey interactions
Am. Nat.
47
1963
209-223