Skip to main content
SpringerLink
Log in

Competing species model with behavioral adaptation

  • Published:
Journal of Mathematical Biology Aims and scope Submit manuscript

Abstract

This paper studies the properties of a modified Lotka-Volterra model for two competing species, in which the coefficients of the interaction terms are time-dependent averages of the level of interaction over the entire past. For this model, it is shown that (1) competitive exclusion does not occur, (2) there are two possible stable equilibrium points, and (3) in a certain region of parameter space numerical simulations suggest the existence of interesting oscillatory solutions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bardi, M.: Predator-prey models in periodically fluctuating environments. J. Math. Biol. 12, 127–138 (1981)

    Google Scholar 

  2. Cushing, J. M.: An operator equation and bounded solutions of integrodifferential systems. SIAM Math. Anal. 6, 433–445 (1975)

    Google Scholar 

  3. Cushing, J. M.: Periodic time-dependent predator-prey systems. SIAM J. Appl. Math. 32, 82–95 (1977)

    Google Scholar 

  4. Hsu, S. B.: On a resource based ecological competition model with interference, J. Math. Biol. 12, 45–52 (1981)

    Google Scholar 

  5. Miller, R. K.: Asymptotic stability and perturbations for linear Volterra integro-differential systems. In: Schmitt, K. (ed.) Delays and functional differential equations and their applications. New York: Academic Press 1972

    Google Scholar 

  6. Noonburg, V. W.: Effects of behavioral adaptation on a predator-prey model. J. Math. Biol. 15, 239–247 (1982)

    Google Scholar 

  7. Smith, H. L.: The interaction of steady-state and Hopf bifurcations in a two-predator-one-prey competition model. SIAM J. Appl. Math. 42, 27–33 (1982)

    Google Scholar 

  8. Volterra, V.: Leçon sur la théorie mathématique de la lutte pour la vie. Paris: Gauthier-Villars 1931

    Google Scholar 

  9. Waltman, P.: Competition models in population biology. CBMS-NSF Regional Conference Series in Applied Mathematics 45. SIAM, Philadelphia 1983

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Cornell University, 14853, Ithaca, NY, USA

    V. W. Noonburg

  2. Department of Mathematics, University of Hartford, West Hartford, CT, USA

    V. W. Noonburg

Authors
  1. V. W. Noonburg
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Noonburg, V.W. Competing species model with behavioral adaptation. J. Math. Biology 24, 543–555 (1986). https://doi.org/10.1007/BF00275683

Download citation

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00275683

Key words

Search

Navigation