\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

A boundary value problem for integrodifference population models with cyclic kernels

Abstract / Introduction Related Papers Cited by
  • The population dynamics of species with separate growth and dispersal stages can be modeled by a discrete-time, continuous-space integrodifference equation. Many authors have considered the case where the model parameters remain fixed over time, however real environments are constantly in flux. We develop a framework for analyzing the population dynamics when the dispersal parameters change over time in a cyclic fashion. In particular, for the case of $N$ cyclic dispersal kernels modeling movement in the presence of unidirectional flow, we derive a $2N^{th}$-order boundary value problem that can be used to study the linear stability of the associated integrodifference model.
    Mathematics Subject Classification: Primary: 45C05, 92B05; Secondary: 34B05.

    Citation:

    \begin{equation} \\ \end{equation}
  • [1]

    C. J. Collins, C. I. Fraser, A. Ashcroft and J. M. Waters, Asymmetric dispersal of southern bull-kelp (Durvillaea antarctica) adults in coastal New Zealand: Testing and oceanographic hypothesis, Molecular Ecology, 19 (2010), 4572-4580.doi: 10.1111/j.1365-294X.2010.04842.x.

    [2]

    R. Dirzo and P. H. Raven, Global state of biodiversity and loss, Annual Review of Environment and Resources, 28 (2003), 137-167.

    [3]

    N.-E. Fahssi, Polynomial triangles revisited. arXiv:1202.0228v7 [math.CO], (2012).

    [4]

    D. P. Hardin, P. Takáč and G. F. Webb, Asymptotic properties of a continuous-space discrete-time population model in a random environment, Journal of Mathematical Biology, 26 (1988), 361-374.doi: 10.1007/BF00276367.

    [5]

    M. P. Hassel, The Dynamics of Arthropod Predator-Prey Systems, no. 13 in Monographs in Population Biology, Princeton University Press, 1978.

    [6]

    C. M. Herrera, P. Jordano, J. Guitian and A. Traveset, Annual variability in seed production by woody plants and the masting concept: Reassessment of principles and relationship to pollination and seed dispersal, The American Naturalist, 152 (1998), 576-594.doi: 10.1086/286191.

    [7]

    H. F. Howe and J. Smallwood, Ecology of seed dispersal, Annual Review of Ecology and Systematics, 13 (1982), 201-228.doi: 10.1146/annurev.es.13.110182.001221.

    [8]

    J. Jacobsen, Y. Jin, and M. A. Lewis, Integrodifference models for persistence in temporally varying river environments, preprint. doi: 10.1007/s00285-014-0774-y.

    [9]

    M. Kot and W. M. Schaffer, Discrete-time growth-dispersal models, Mathematical Biosciences, 80 (1986), 109-136.doi: 10.1016/0025-5564(86)90069-6.

    [10]

    M. A. Krasnosel'skii, Positive Solutions of Operator Equations, P. Noordhoff Ltd., Groningen, The Netherlands, 1964.

    [11]

    F. Lutscher, E. Pachepsky and M. A. Lewis, The effect of dispersal patterns on stream populations, SIAM Review, 47 (2005), 749-772.doi: 10.1137/050636152.

    [12]

    M. G. Neubert, M. Kot and M. A. Lewis, Dispersal and pattern-formation in a discrete-time predator-prey model, Theoretical Population Biology, 48 (1995), 7-43.doi: 10.1006/tpbi.1995.1020.

    [13]

    D. Pearce, An economic approach to saving the tropical forests, in Economic Policy Towards the Environment, (ed. D. Helm), Blackwell Publishers, 1991, 239-262.

    [14]

    N. J. A. SloaneOnline Encyclopedia of Integer Sequences, 2013.

    [15]

    C. Tudge, Last Animals at the Zoo: How Mass Extinction Can Be Stopped, Island Press, Washington, D.C., 1992.

    [16]

    R. W. Van Kirk and M. A. Lewis, Integrodifference models for persistence in fragmented habitats, Bulletin of Mathematical Biology, 59 (1997), 107-137.

  • 加载中
SHARE

Article Metrics

HTML views() PDF downloads(118) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return