Bibliography for the Lotka-Volterra Model - short

short

  1. Average growth and extinction in a two dimensional Lotka-Volterra system.
    Ahmad, Shair; Montes de Oca, Francisco
    Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 9 (2002), no. 2, 177--186, MathSciNet.
  2. Global bifurcation structure of stationary solutions for a Lotka-Volterra competition model.
    Kan-on, Yukio
    Discrete Contin. Dyn. Syst. 8 (2002), no. 1, 147--162, MathSciNet.
  3. Limit cycles for the competitive three dimensional Lotka-Volterra system.
    Xiao, Dongmei; Li, Wenxia
    J. Differential Equations 164 (2000), no. 1, 1--15, MathSciNet.
  4. Analytic solutions to a family of Lotka-Volterra related differential equations.
    Evans, C. M.; Findley, G. L.
    J. Math. Chem. 25 (1999), no. 2-3, 181--189
  5. Oscillations and Chaos behind Predator-Prey Invasion: Mathematical Artifact or Ecological Reality?  
    Jonathan A. Sherratt, Barry T. Eagan, Mark A. Lewis  
    Philosophical Transactions: Biological Sciences, Vol. 352, No. 1349. (Jan. 29, 1997), pp. 21-38, Jstor.
  6. Soil Food Webs and Ecosystem Processes: Decomposition in Donor-Control and Lotka-Volterra Systems  
    David W. Zheng, Jan Bengtsson, Goran I. Agren  
    American Naturalist, Vol. 149, No. 1. (Jan., 1997), pp. 125-148, Jstor.
  7. Predator-Induced Breeding Suppression and Its Consequences for Predator-Prey Population Dynamics  
    Graeme D. Ruxton, Steven L. Lima  
    Proceedings: Biological Sciences, Vol. 264, No. 1380. (Mar. 22, 1997), pp. 409-415, Jstor.
  8. Can Sublethal Parasitism Destabilize Predator-Prey Population Dynamics? A Model of Snowshoe Hares, Predators and Parasites  
    Anthony R. Ives, Dennis L. Murray  
    Journal of Animal Ecology, Vol. 66, No. 2. (Mar., 1997), pp. 265-278, Jstor.
  9. Predator-Prey Instability: Individual-Level Mechanisms for Population-Level Results  
    B. E. Beisner, E. McCauley, F. J. Wrona  
    Functional Ecology, Vol. 11, No. 1. (Feb., 1997), pp. 112-120, Jstor.
  10. Dynamic Ideal Free Distribution: Effects of Optimal Patch Choice on Predator-Prey Dynamics  
    Vlastimil Krivan  
    American Naturalist, Vol. 149, No. 1. (Jan., 1997), pp. 164-178, Jstor.
  11. Old and new results on Lotka-Volterra systems.
    Redheffer, Raymond
    Proceedings of the Second World Congress of Nonlinear Analysts, Part 6 (Athens, 1996). Nonlinear Anal. 30 (1997), no. 6, 3207--3213, MathSciNet.
  12. Extinction in Nonautonomous Competitive Lotka-Volterra Systems  
    Francisco Montes de Oca, Mary Lou Zeeman  
    Proceedings of the American Mathematical Society, Vol. 124, No. 12. (Dec., 1996), pp. 3677-3687, Jstor.
  13. Connection between the Existence of First Integrals and the Painleve Property in Two-Dimensional Lotka-Volterra and Quadratic Systems  
    D. D. Hua, L. Cairo, M. R. Feix, K. S. Govinder, P. G. L. Leach  
    Proceedings: Mathematical, Physical and Engineering Sciences, Vol. 452, No. 1947. (Apr. 9, 1996), pp. 859-880, Jstor.
  14. On directed periodic orbits in three-dimensional competitive Lotka-Volterra systems.
    Zeeman, Mary Lou
    Differential equations and applications to biology and to industry (Claremont, CA, 1994), 563--572, World Sci. Publishing, River Edge, NJ, 1996
  15. Extinction in Competitive Lotka-Volterra Systems  
    Mary Lou Zeeman  
    Proceedings of the American Mathematical Society, Vol. 123, No. 1. (Jan., 1995), pp. 87-96, Jstor.
  16. Global Stability for a Class of Predator-Prey Systems  
    Sze-Bi Hsu, Tzy-Wei Huang  
    SIAM Journal on Applied Mathematics, Vol. 55, No. 3. (Jun., 1995), pp. 763-783, Jstor.
  17. Balancing survival and extinction in nonautonomous competitive Lotka-Volterra systems.
    Montes de Oca, F.; Zeeman, M. L.
    J. Math. Anal. Appl. 192 (1995), no. 2, 360--370, MathSciNet.
  18. An Accurate Solution to the Multispecies Lotka-Volterra Equations (in Classroom Notes)  
    Shmuel Olek  
    SIAM Review, Vol. 36, No. 3. (Sep., 1994), pp. 480-488, Jstor.
  19. On the Nonautonomous Volterra-Lotka Competition Equations  
    Shair Ahmad  
    Proceedings of the American Mathematical Society, Vol. 117, No. 1. (Jan., 1993), pp. 199-204, Jstor.
  20. Loose Coupling of Predator-Prey Cycles: Entrainment, Chaos, and Intermittency in the Classic Macarthur Consumer-Resource Equations  
    John Vandermeer  
    American Naturalist, Vol. 141, No. 5. (May, 1993), pp. 687-716, Jstor.
  21. Diffusion-Induced Chaos in a Spatial Predator--Prey System  
    Mercedes Pascual  
    Proceedings: Biological Sciences, Vol. 251, No. 1330. (Jan. 22, 1993), pp. 1-7, Jstor.
  22. Dynamics of Age-Structured and Spatially Structured Predator-Prey Interactions: Individual-Based Models and Population-Level Formulations  
    Edward McCauley, William G. Wilson, Andre M. de Roos  
    American Naturalist, Vol. 142, No. 3. (Sep., 1993), pp. 412-442, Jstor.
  23. Self-Assembling Food Webs: A Global Viewpoint of Coexistence of Species in Lotka-Volterra Communities  
    Richard Law, Jerry C. Blackford  
    Ecology, Vol. 73, No. 2. (Apr., 1992), pp. 567-578, Jstor.
  24. The Coevolution of Predator--Prey Interactions: ESSS and Red Queen Dynamics  
    Paul Marrow, Richard Law, C. Cannings  
    Proceedings: Biological Sciences, Vol. 250, No. 1328. (Nov. 23, 1992), pp. 133-141, Jstor.
  25. Mobility Versus Density-Limited Predator--Prey Dynamics on Different Spatial Scales  
    Andre M. De Roos, Edward Mccauley, William G. Wilson  
    Proceedings: Biological Sciences, Vol. 246, No. 1316. (Nov. 22, 1991), pp. 117-122, Jstor.
  26. Bionomic exploitation of Lotka-Volterra prey-predator system.
    Chaudhuri, K. S.; Ray, Sumita Saha
    Bull. Calcutta Math. Soc. 83 (1991), no. 2, 175--186, MathSciNet.
  27. Stochastic Structure and Nonlinear Dynamics of Food Webs: Qualitative Stability in a Lotka-Volterra Cascade Model  
    J. E. Cohen, T. Luczak, C. M. Newman, Z.-M. Zhou  
    Proceedings of the Royal Society of London. Series B, Biological Sciences, Vol. 240, No. 1299. (Jun. 22, 1990), pp. 607-627, Jstor.
  28. Oscillations in Lotka-Volterra systems of chemical reactions.
    Hering, Roger H.
    J. Math. Chem. 5  (1990), no. 2, 197--202
  29. A Neural Network Modeled by an Adaptive Lotka-Volterra System  
    V. W. Noonburg  
    SIAM Journal on Applied Mathematics, Vol. 49, No. 6. (Dec., 1989), pp. 1779-1792, Jstor.
  30. A Lotka-Volterra's system of reaction-diffusion equations with time lag in ecology.
    Ding, Chong Wen
    Ann. Differential Equations 5 (1989), no. 2, 129--143
  31. Global Asymptotic Stability of Lotka-Volterra Diffusion Models with Continuous Time Delay  
    E. Beretta, Y. Takeuchi  
    SIAM Journal on Applied Mathematics, Vol. 48, No. 3. (Jun., 1988), pp. 627-651, Jstor.
  32. Stability and Hopf Bifurcation in a Predator-Prey System with Several Parameters  
    J. Hainzl  
    SIAM Journal on Applied Mathematics, Vol. 48, No. 1. (Feb., 1988), pp. 170-190, Jstor.
  33. Bifurcations and Transitions to Chaos in the Three-Dimensional Lotka- Volterra Map  
    L. Gardini, R. Lupini, C. Mammana, M. G. Messia  
    SIAM Journal on Applied Mathematics, Vol. 47, No. 3. (Jun., 1987), pp. 455-482, Jstor.
  34. Antipredator Behavior and the Population Dynamics of Simple Predator-Prey Systems  
    Anthony R. Ives, Andrew P. Dobson  
    American Naturalist, Vol. 130, No. 3. (Sep., 1987), pp. 431-447, Jstor.
  35. Periodic solutions of periodically harvested Lotka-Volterra systems.
    Hausrath, Alan R.; Manásevich, Raúl F.
    Rev. Colombiana Mat. 21 (1987), no. 2-4, 337--345.
  36. Bifurcation phenomena appearing in the Lotka-Volterra competition equations: a numerical study.
    Namba, Toshiyuki
    Math. Biosci. 81 (1986), no. 2, 191--212.
  37. Infectious Disease and Species Coexistence: A Model of Lotka-Volterra Form  
    Robert D. Holt, John Pickering  
    American Naturalist, Vol. 126, No. 2. (Aug., 1985), pp. 196-211, Jstor.
  38. Continuous Lotka-Volterra models for evolution processes.
    Ebeling, W.; Feistel, R.
    Lotka-Volterra-approach to cooperation and competition in dynamic systems (Eisenach, 1984), 55--62, Math. Res., 23, Akademie-Verlag, Berlin, 1985.
  39. Stable Coexistence States in the Volterra-Lotka Competition Model with Diffusion  
    Chris Cosner, A. C. Lazer  
    SIAM Journal on Applied Mathematics, Vol. 44, No. 6. (Dec., 1984), pp. 1112-1132, Jstor.
  40. Stable Coexistence States in the Volterra-Lotka Competition Model with Diffusion  
    Chris Cosner, A. C. Lazer  
    SIAM Journal on Applied Mathematics, Vol. 44, No. 6. (Dec., 1984), pp. 1112-1132, Jstor.
  41. Traveling Wave Solutions of Diffusive Lotka-Volterra Equations: A Heteroclinic Connection in R^4  
    Steven R. Dunbar
    Transactions of the American Mathematical Society, Vol. 286, No. 2. (Dec., 1984), pp. 557-594, Jstor.
  42. Scenarios leading to chaos in a forced Lotka-Volterra model.
    Inoue, Masayoshi; Kamifukumoto, Hiroshi
    Progr. Theoret. Phys. 71 (1984), no. 5, 930--937
  43. The Period in the Volterra-Lotka Predator-Prey Model  
    Jorg Waldvogel  
    SIAM Journal on Numerical Analysis, Vol. 20, No. 6. (Dec., 1983), pp. 1264-1272, Jstor.
  44. Stable spatio-temporal oscillations of diffusive Lotka-Volterra system with three or more species.
    Kishimoto, Kazuo; Mimura, M.; Yoshida, K.
    J. Math. Biol. 18 (1983), no. 3, 213--221
  45. Dispersal and the Stability of Predator-Prey Interactions  
    Philip H. Crowley  
    American Naturalist, Vol. 118, No. 5. (Nov., 1981), pp. 673-701, Jstor.
  46. Three-step food chains in Gompertz and Lotka-Volterra models.
    Bhat, Nalini; Pande, L. K.
    J. Theoret. Biol. 91 (1981), no. 3, 429--435
  47. Stability in a One-Predator-Three-Prey Community  
    Roger A. Powell  
    American Naturalist, Vol. 115, No. 4. (Apr., 1980), pp. 567-579, Jstor.
  48. Conditions for Global Stability Concerning a Prey-Predator Model with Delay Effects  
    Anthony Leung  
    SIAM Journal on Applied Mathematics, Vol. 36, No. 2. (Apr., 1979), pp. 281-286, Jstor.
  49. Convergence to Homogeneous Equilibrium State for Generalized Volterra-Lotka Systems with Diffusion  
    P. De Mottoni, F. Rothe  
    SIAM Journal on Applied Mathematics, Vol. 37, No. 3. (Dec., 1979), pp. 648-663, Jstor.
  50. Waterboatmen, and Testing for Lotka-Volterra-Type Interactions (in Letters to the Editors)  
    Marc Bergmans  
    American Naturalist, Vol. 113, No. 5. (May, 1979), pp. 759-761, Jstor.
  51. Spiral Chaos in a Predator-Prey Model (in Letters to the Editors)  
    Michael E. Gilpin  
    American Naturalist, Vol. 113, No. 2. (Feb., 1979), pp. 306-308, Jstor.
  52. A note on the global stability and bifurcation phenomenon of a Lotka-Volterra food chain.
    So, Joseph W. H.
    J. Theoret. Biol. 80 (1979), no. 2, 185--187
  53. Lotka-Volterra Population Models  
    Peter J. Wangersky  
    Annual Review of Ecology and Systematics, Vol. 9. (1978), pp. 189-218, Jstor.
  54. A More Functional Response to Predator-Prey Stability (in Letters to the Editors)  
    Simon A. Levin  
    American Naturalist, Vol. 111, No. 978. (Mar. - Apr., 1977), pp. 381-383, Jstor.
  55. On Lotka-Volterra predator prey models.
    Billard, L.
    J. Appl. Probability 14 (1977), no. 2, 375--381
  56. Concepts of Stability and Resilience in Predator-Prey Models  
    J. R. Beddington, C. A. Free, J. H. Lawton  
    Journal of Animal Ecology, Vol. 45, No. 3. (Oct., 1976), pp. 791-816, Jstor.
  57. Functional Response and Stability in Predator-Prey Systems  
    Allan Oaten, William W. Murdoch  
    American Naturalist, Vol. 109, No. 967. (May - Jun., 1975), pp. 289-298, Jstor.
  58. Switching, Functional Response, and Stability in Predator-Prey Systems  
    Allan Oaten, William W. Murdoch  
    American Naturalist, Vol. 109, No. 967. (May - Jun., 1975), pp. 299-318, Jstor.
  59. A Biological Least-Action Principle for the Ecological Model of Volterra-Lotka  
    Paul A. Samuelson  
    Proceedings of the National Academy of Sciences of the United States of America, Vol. 71, No. 8. (Aug., 1974), pp. 3041-3044, Jstor.
  60. A biological least-action principle for the ecological model of Volterra-Lotka.
    Samuelson, Paul A.
    Proc. Nat. Acad. Sci. U.S.A. 71 (1974), 3041--3044
  61. The Stability of Predator-Prey Systems  
    J. Maynard Smith, M. Slatkin  
    Ecology, Vol. 54, No. 2. (Mar., 1973), pp. 384-391, Jstor.
  62. Enriched Predator-Prey Systems: Theoretical Stability (in Reports)  
    Michael E. Gilpin, M. L. Rosenzweig  
    Science, New Series, Vol. 177, No. 4052. (Sep. 8, 1972), pp. 902-904, Jstor.
  63. A Markov Contingency-Table Model for Replicated Lotka-Volterra Systems Near Equilibrium  
    Joel E. Cohen  
    American Naturalist, Vol. 104, No. 940. (Nov. - Dec., 1970), pp. 547-560, Jstor.
  64. Variation in the Availability of Food as a Cause of Fluctuations in Predator and Prey Population Densities  
    A. L. Jensen, R. C. Ball  
    Ecology, Vol. 51, No. 3. (May, 1970), pp. 517-520, Jstor.
  65. Graphical Representation and Stability Conditions of Predator-Prey Interactions  
    M. L. Rosenzweig, R. H. MacArthur  
    American Naturalist, Vol. 97, No. 895. (Jul. - Aug., 1963), pp. 209-223, Jstor.
  66. Time Lag in Prey-Predator Population Models  
    Peter J. Wangersky, W. J. Cunningham  
    Ecology, Vol. 38, No. 1. (Jan., 1957), pp. 136-139, Jstor.

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2003