ON A NEW MODEL OF TWO-PATCH PREDATOR-PREY SYSTEM WITH MIGRATION OF BOTH SPECIES

Wei Feng; Brevin Rock; Jody Hinson

doi:10.11948/2011013

2011 Volume 1 Issue 2

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Wei Feng, Brevin Rock, Jody Hinson. ON A NEW MODEL OF TWO-PATCH PREDATOR-PREY SYSTEM WITH MIGRATION OF BOTH SPECIES[J]. Journal of Applied Analysis & Computation, 2011, 1(2): 193-203. doi: 10.11948/2011013

Citation:

Wei Feng, Brevin Rock, Jody Hinson. ON A NEW MODEL OF TWO-PATCH PREDATOR-PREY SYSTEM WITH MIGRATION OF BOTH SPECIES[J]. Journal of Applied Analysis & Computation, 2011, 1(2): 193-203. doi: 10.11948/2011013

ON A NEW MODEL OF TWO-PATCH PREDATOR-PREY SYSTEM WITH MIGRATION OF BOTH SPECIES

1 Department of Mathematics and Statistics, UNC Wilmington, Wilmington, NC 28403, USA;
2 Department of Mathematics and Physical Education, Cape Fear Community College, 411 N Front Street, Wilmington, NC 28401, USA

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Abstract

Abstract

In this paper we explore the dynamics of predator-prey in a two patch system. The two patches of the system are coupled with both the migration of the predator and the prey. The purpose of this exploration is to find upper and lower bounds for the populations and get an insight on the different possibilities with the three types of Holling functional responses. Also we discuss the stability and instability of the equilibrium solutions found in earlier papers. Numerical simulations are provided to graphically demonstrate the population dynamics of the system.
- Predator-prey models /
- two-patch migrations /
- extinction or coexistence /
- stability and asymptotic behavior /
- numerical simulations
MSC: 35K55;35B40

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References

[1]	T. Alligood, T. D. Sauer and J. A. Yorke, Chaos:An Introduction to Dynamical Systems, Springer-Verlag, New York, 1996. Google Scholar
[2]	C. Cosner, d. L. DeAngelis, J. S. Ault and D. B. Olson, Effects of spatial grouping on the function response of predators, Theoretical Population Biology, 56(1999), 65-75. Google Scholar
[3]	L. Edelstein-Keshet, Mathematical Models in Biology, McGraw-Hill Inc., New York, 1977. Google Scholar
[4]	W. Feng and J. Hinson, Stability and pattern in two-patch predator-prey population dynamics, Discrete and Continuous Dynamical Systems, Added Volume(2005), 268-279. Google Scholar
[5]	W. Feng, X. Lu and R. J. Donavan, Population dynamics in a model for territory acquisition, Discrete and Continuous Dynamical Systems, Added Volume(2001), 156-165. Google Scholar
[6]	W. Feng, Competitive exclusion and persistence in models of resource and sexual competition, J. Math. Biology, 35(1997), 683-694. Google Scholar
[7]	W. Feng and X. Lu, Global periodicity in a class of reaction-diffusion systems with time delays, Discrete and Continuous Dynamical Systems, B3(2003), 69-78. Google Scholar
[8]	W. S. C. Gurney and R. M Nesbet, Ecological Dynamics, Oxford University Press, 1998. Google Scholar
[9]	V. A. A. Jansen, Theoretical Aspects of Metapopulation Dynamcs, Ph. D. thesis, Leiden University, The Netherlands, 1994. Google Scholar
[10]	V. A. A. Jansen, Regulation of predator-prey systems through spatial interactions:a possible solution to the paradox of nrichment, Oikos, 74(1995), 384-390. Google Scholar
[11]	V. A. A. Jansen and A. M. DeRoos, The Role of space in reducing predatorprey cycles, in "The Geometry of Ecological Interactions Simplifying Spacial Compelxity", Cambridge University Press, (2000), 183-201. Google Scholar
[12]	V. A. A. Jansen and A. L. Lloyd, Local stability analysis of spatially homogenous solutions of multi-patch systems, Journal of Mathematical Biology, 41(2000), 232-252. Google Scholar
[13]	V. A. A. Jansen, The dynamics of two diffusively coupled predator-prey populations, Theoretical Population Biology, 59(2001), 119-131. Google Scholar
[14]	C. Lu, W. Feng and X. Lu, Long-term survival in a 3-species ecological system, Dynamics of Continuous, Discrete and Impulsive Systems, 3(1997), 199-213. Google Scholar
[15]	J. D. Murray, Lectures on Nonlinear-Differential-Equation Models in Biology, Oxford University Press, Oxford, 1977. Google Scholar
[16]	J. D. Murray, Mathematical Biology, Springer-Verlag, Berlin, 1993. Google Scholar
[17]	J. T. Rowell and W. Feng, Population dynamics in complex predator-prey interactions, Proceedings of Dynamic Systems and Applications, 2(1996), 493-500. Google Scholar