Abstract
Any organism in nature will inevitably be affected by uncertain factors. The deterministic model and stochastic model are no longer suitable for population dynamics analysis under uncertain noise environment. In order to simulate these problems more reasonably, we propose an uncertain logistic population model with Allee effect, which describes the population dynamic behavior through uncertain differential equation. In this paper, the solution and \(\alpha\)-path of the uncertain Logistic population model with Allee effect are given, and the behavior analysis of the solution is also discussed. Besides, some numerical examples are put forward to illustrate the conclusions obtained in the paper.
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References
Allee WC (1931) Animal aggregations. University of Chicago Press, Chicago
Dennis B, Assas L, Elaydi S, Kwessi E, Livadiotis G (2016) Allee effects and resilience in stochastic populations. Theor Ecol 9(3):323–335
Ji WM (2020) On a population model with Allee effects and environmental perturbations. J Appl Math Comput 64(1–2):749–764
Ji WM, Zhang YQ, Liu M (2021) Dynamical bifurcation and explicit stationary density of a stochastic population model with Allee effects. Appl Math Lett 111(2021):106662
Li SG, Peng J, Zhang B (2015) Multifactor uncertain differential equation. J Uncertain Anal Appl 3(7):1–19
Liu B (2007) Uncertainty theory, 2nd edn. Springer, Berlin
Liu B (2008) Fuzzy process, hybrid process and uncertain process. J Uncertain Syst 2(1):3–16
Liu B (2009) Some research problems in uncertainty theory. J Uncertain Syst 3(1):3–10
Liu B (2010) Uncertainty theory: a branch of mathematics for modeling human uncertainty. Springer, Berlin
Liu YH, Ha MH (2010) Expected value of function of uncertain variables. J Uncertain Syst 4(3):181–186
Sheng YH, Gao R, Zhang ZQ (2017) Uncertain population model with age-structure. J Intell Fuzzy Syst 33(2):853–858
Yang XF, Gao J (2013) Uncertain differential games with application to capitalism. J Uncertain Anal Appl 1(17):1–11
Yang XF, Yao K (2017) Uncertain partial differential equation with application to heat conduction. Fuzzy Optim Decis Mak 16(3):379–403
Yao K (2012) Uncertain calculus with renewal process. Fuzzy Optim Decis Mak 11(3):285–297
Yao K (2013) Extreme value and integral of solution of uncertain differential equation. J Uncertain Anal Appl 1(2):1–21
Yao K (2015) Uncertain differential equation with jumps. Soft Comput 19(7):2063–2069
Yao K (2016) Uncertain differential equation. Springer, Berlin
Yao K, Chen XW (2013) A numerical method of solving uncertain differential equations. J Intell Fuzzy Syst 25(3):825–832
Yao K, Liu B (2020) Parameter estimation in uncertain differential equations. Fuzzy Optim Decis Mak 19(1):1–12
Zhang ZQ, Yang XF (2018) Uncertain population model. Soft Comput 24(4):2417–2423
Zhu YG (2015) Uncertain fractional differential equations and an interest rate model. Math Method Appl Sci 38(15):3359–3368
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CG proposed the model and derived the main result of the paper. ZZ helps to polish English and the structure of the paper. Baoliang Liu’s contribution is to present the example and the figures.
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Gao, C., Zhang, Z. & Liu, B. Uncertain Logistic population model with Allee effect. Soft Comput 27, 11091–11098 (2023). https://doi.org/10.1007/s00500-023-08673-0
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DOI: https://doi.org/10.1007/s00500-023-08673-0