DOI QR코드

DOI QR Code

A MODIFIED PREY-PREDATOR MODEL WITH COUPLED RATES OF CHANGE

  • HAN, HYEJI (DEPARTMENT OF MATHEMATICS, GYEONGSANG NATIONAL UNIVERSITY) ;
  • KIM, GWANGIL (DEPARTMENT OF MATHEMATICS, GYEONGSANG NATIONAL UNIVERSITY) ;
  • OH, SEOYOUNG (DEPARTMENT OF MATHEMATICS, GYEONGSANG NATIONAL UNIVERSITY)
  • 투고 : 2021.11.15
  • 심사 : 2021.12.20
  • 발행 : 2021.12.25

초록

The prey-predator model is one of the most influential mathematical models in ecology and evolutionary biology. In this study, we considered a modified prey-predator model, which describes the rate of change for each species. The effects of modifications to the classical prey-predator model are investigated here. The conditions required for the existence of the first integral and the stability of the fixed points are studied. In particular, it is shown that the first integral exists only for a subset of the model parameters, and the phase portraits around the fixed points exhibit physically relevant phenomena over a wide range of the parameter space. The results show that adding coupling terms to the classical model widely expands the dynamics with great potential for applicability in real-world phenomena.

키워드

과제정보

This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korean government(MSIT) (No.NRF-2021R1I1A3048350).

참고문헌

  1. Alfred J Lotka. Analytical note on certain rhythmic relations in organic systems. Proceedings of the National Academy of Sciences, 6(7):410-415, 1920.
  2. Vito Volterra. Variations and fluctuations of the number of individuals in animal species living together. Animal ecology, pages 409-448, 1926.
  3. Alan A Berryman. The orgins and evolution of predator-prey theory. Ecology, 73(5):1530-1535, 1992. https://doi.org/10.2307/1940005
  4. Michael L Rosenzweig and Robert H MacArthur. Graphical representation and stability conditions of predator-prey interactions. The American Naturalist, 97(895):209-223, 1963. https://doi.org/10.1086/282272
  5. Amartya Das and GP Samanta. Modeling the fear effect on a stochastic prey-predator system with additional food for the predator. Journal of Physics A: Mathematical and Theoretical, 51(46):465601, 2018. https://doi.org/10.1088/1751-8121/aae4c6
  6. Scott Creel and David Christianson. Relationships between direct predation and risk effects. Trends in ecology & evolution, 23(4):194-201, 2008. https://doi.org/10.1016/j.tree.2007.12.004
  7. Barbara L Peckarsky, Cathy A Cowan, Marjory A Penton, and Chester Anderson. Sublethal consequences of stream-dwelling predatory stoneflies on mayfly growth and fecundity. Ecology, 74(6):1836-1846, 1993. 36-1846, 1993. https://doi.org/10.2307/1939941
  8. Sourav Kumar Sasmal. Population dynamics with multiple allee effects induced by fear factors-a mathematical study on prey-predator interactions. Applied Mathematical Modelling, 64:1-14, 2018. https://doi.org/10.1016/j.apm.2018.07.021
  9. Sudeshna Mondal, Alakes Maiti, and GP Samanta. Effects of fear and additional food in a delayed predator-prey model. Biophysical Reviews and Letters, 13(04):157-177, 2018. https://doi.org/10.1142/S1793048018500091
  10. Shyam Pada Bera, Alakes Maiti, and Guruprasad Samanta. Stochastic analysis of a prey-predator model with herd behaviour of prey. Nonlinear Analysis: Modelling and Control, 21(3):345-361, 2016. https://doi.org/10.15388/NA.2016.3.4
  11. Pablo Aguirre, Eduardo Gonzalez-Olivares, and Soledad Torres. Stochastic predator-prey model with allee ' effect on prey. Nonlinear Analysis: Real World Applications, 14(1):768-779, 2013. https://doi.org/10.1016/j.nonrwa.2012.07.032
  12. Amartya Das and GP Samanta. Stochastic prey-predator model with additional food for predator. Physica A: Statistical Mechanics and its Applications, 512:121-141, 2018. https://doi.org/10.1016/j.physa.2018.08.138