Issue |
Math. Model. Nat. Phenom.
Volume 15, 2020
Ecology and evolution
|
|
---|---|---|
Article Number | 46 | |
Number of page(s) | 18 | |
DOI | https://doi.org/10.1051/mmnp/2019055 | |
Published online | 24 September 2020 |
- P. Aguirre, E. González-Olivares, S. Torres, Stochastic predator-prey model with Allee effect on prey. Nonlinear Anal. Real World Appl. 14 (2013) 768–779. [Google Scholar]
- W. Allee, Animal aggregations: A study in general sociology, University of Chicago Press, Chicago (1931). [CrossRef] [Google Scholar]
- J. Bao, J. Shao, Permanence and extinction of regime-switching predator-prey models. J. Math. Anal. 48 (2015) 725–739. [Google Scholar]
- Y. Cai, X. Mao, A stochastic prey-predator model with time-dependent delays. Appl. Math. Model. 64 (2018) 357–371. [Google Scholar]
- J. Chattopadhyay, O. Arino, A predator-prey model with disease in the prey. Nonlinear Anal. 36 (1999) 747–766. [CrossRef] [MathSciNet] [Google Scholar]
- T. Chowdhury, S. Chakraborty, J. Chattopadhyay, Migratory effect of middle predator in a tri-trophic food chain model. Math. Methods Appl. Sci. 33 (2010) 1699–1711. [Google Scholar]
- N. Dang, N. Du, T. Ton, Asymptotic behavior of predator-prey systems perturbed by white noise. Acta Appl. Math. 115 (2011) 351–370. [Google Scholar]
- A. Das, G. Samanta, Stochastic prey-predator model with additional food for predator. Physica A 512 (2018) 121–141. [Google Scholar]
- P. DeBach, Biological Control by Natural Enemies, Cambridge University Press, UK, (1974). [Google Scholar]
- S. Ghorai, S. Poria, Impacts of additional food on diffusion induced instabilities in a predator-prey system with mutually interfering predator. Chaos Solitons Fractals 103 (2017) 68–78. [Google Scholar]
- E. González-Olivares, R. Ramos-Jiliberto, Dynamic consequences of prey refuges in a simple model system: more prey, fewer predators and enhanced stability. Ecol. Model. 166 (2003) 135–146. [CrossRef] [Google Scholar]
- Q. Han, D. Jiang, C. Ji, Analysis of a delayed stochastic predator-prey model in a polluted environment. Appl. Math. Model. 38 (2014) 3067–3080. [Google Scholar]
- R.Z. Hasminskii, Stochastic Stability of Differential Equations. Sijthoff and Noordhoff, Maryland (1980). [CrossRef] [Google Scholar]
- D. Higham, An algorithmic introduction to numerical simulation of stochastic differential equations. SIAM. Rev. 43 (2001) 525–546. [CrossRef] [MathSciNet] [Google Scholar]
- C. Holling, Some characteristics of simple types of predation and parasitism. Mem. Entomol. Soc. Canada 46 (1965) 1–60. [Google Scholar]
- D. Kumar, S. Chakrabarty, A predator-prey model with additional food supply to predators: dynamics and applications. J. Comp. Appl. Math. 37 (2018) 763–784. [Google Scholar]
- A. Lahrouz, A. Settati, P.S. Mandal, Dynamics of a switching diffusion modified Leslie Gower Predator-prey system with Beddington-DeAngelis functional response. Nonlinear Dynam. 85 (2016) 853–870. [CrossRef] [Google Scholar]
- M. Liu, X. He, J. Yu, Dynamics of a stochastic regime-switching predator-prey model with harvesting and distributed delays. Nonlinear Anal. Hybrid. 28 (2018) 87–104. [CrossRef] [Google Scholar]
- R. Liu, G. Liu, Analysis of a stochastic predator-prey population model with Allee effect and jumps. J. Inequal. Appl. 60 (2019) 1–16. [Google Scholar]
- A. Lotka, Analytical note on certain rhythmic relations in organic systems. Proc. Natl. Acad. Sci. 6 (1920) 410–415. [CrossRef] [PubMed] [Google Scholar]
- X. Mao, Stochastic Differential Equations and Applications. Horwood Publishing, Chichester (1997). [Google Scholar]
- R. May, Stability in randomly fluctuating versus deterministic environments. Am. Nat. 107 (1973) 621–650. [Google Scholar]
- J. Margaritopoulos, J. Tsitsipis, D. Perdikis, Biological characteristics of the mirids Macrolophus costalis and Macroplophus pygmaeus preying on the tobacco form of Myzus persicae (Hemiptera: Aphididae). B. Entomol. Res. 93 (2003) 39. [CrossRef] [Google Scholar]
- B. Sahoo, S. Poria, Effects of additional food in a delayed predator-prey model. Math. Biosc. 261 (2015) 62–73. [CrossRef] [Google Scholar]
- P. Srinivasu, B. Prasad, Role of quantity of additional food to predators as a control in predator-prey systems with relevance to pest management and biological conservation. Bull. Math. Biol. 73 (2011) 2249–2276. [Google Scholar]
- P. Srinivasu, D. Vamsi, V. Ananth, Additional food supplements as a tool for biological conservation of predator-prey systems involving type III functional response: A qualitative and quantitative investigation. J. Theor. Biol. 455 (2018) 303–318. [CrossRef] [PubMed] [Google Scholar]
- V. Volterra, Variazioni e fluttuazioni del numero d’individui in specie d’animali conviventi. Mem. Acad. Lincei 2 (1989) 31–113. [Google Scholar]
- G. Yin, C. Zhu, Asymptotic properties of hybrid diffusion systems. SIAM J. Control Optim. 46 (2007) 1155–1179. [Google Scholar]
- G. Yin, C. Zhu, Hybrid Switching Diffusions Properties and Applications. Springer-Verlag, New York (2009). [Google Scholar]
- L. Zu, D. Jiang, D. O’Regand, T. Hayat, Ergodic property of a Lotka-Volterra predator-prey model with white noise higher order perturbation under regime switching. Appl. Math. Comput. 330 (2018) 93–102. [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.