Abstract
Considering that the population size is always influenced by various uncertain factors in varying environment, we present some new types of uncertain population models: uncertain population growth model and uncertain logistic population growth model which are described by uncertain differential equations. And some properties of these uncertain population models are discussed within the framework of uncertainty theory.
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References
Barbacioru IC (2010) Uncertainty functional differential equations for finance. Surv Math Appl 5:275–284
Chen XW, Liu B (2010) Existence and uniqueness theorem for uncertain differential equations. Fuzzy Optim Decis Mak 9(1):69–81
Chen XW (2011) American option pricing formula for uncertain financial market. Int J Oper Res 8(2):32–37
Chen XW, Gao J (2013) Uncertain term structure model of interest rate. Soft Comput 17(4):597–604
Chen XW, Liu YH, Ralescu DA (2013) Uncertain stock model with periodic dividends. Fuzzy Optim Decis Mak 12(1):111–123
Chen XW, Ralescu DA (2013) Liu process and uncertain calculus. J Uncertain Anal Appl, vol 1, Article 3
Engen S (2007) Stochastic growth and extinction in spatial geometric Brownian population model with migration and correlated noise. Math Biosci 209:240–255
Feller W (1951) Diffusion processes in Genetics. In: Second Berkely symposium on mathematical statistics and probability, pp 227–246
Gao R (2017) Uncertain wave equation with infinite half-boundary. Appl Math Comput 304:28–40
Ge XT, Zhu Y (2012) Existence and uniqueness theorem for uncertain delay differential equations. J Comput Inf Syst 8(20):8341–8347
Li SG, Peng J, Zhang B (2015) Multifactor uncertain differential equation. J Uncertain Anal Appl, vol 3, Article 7
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 B (2014) Uncertainty distribution and independence of uncertain processes. Fuzzy Optim Decis Mak 13(3):259–271
Liu HJ, Fei WY (2013) Neutral uncertain delay differential equation. Inf Int Interdiscip J 16(2):1225–1232
Liu YH, Ha MH (2010) Expected value of function of uncertain variables. J Uncertain Syst 4(3):181–186
Liu YH, Chen XW, Ralescu DA (2015) Uncertain currency model and currency option pricing. Int J Intell Syst 30:40–51
Matis JH, Kiffe TR (2000) Stochastic population models: a compartmental perspective. Springer, New York
Peng J, Yao K (2011) A new option pricing model for stocks in uncertainty markets. Int J Oper Res 8(2):18–26
Soboleva TK, Pleasants AB (2003) Population growth as a nonlinear stochastic process. Math Comput Modell 38:1437–1442
Sun JJ, Chen XW (2015) Asian option pricing formulas for uncertain financial market. J Uncertain Anal Appl, vol 3, Article 11
Verhulst PF (1838) Notice sur la loi que la population suit dans son accroissement. Corresp Math Phys 10:113–121
Yang XF, Gao J (2013) Uncertain differential games with application to capitalism. J Uncertain Anal Appl, vol 1, Article 17
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, Chen XW (2013) A numerical method for solving uncertain differential equations. J Intell Fuzzy Syst 25(3):825–832
Yao K (2013) Extreme values and integral of solution of uncertain differential equation. J Uncertain Anal Appl, vol 1, Article 2
Yao K (2016) Uncertain differential equation. Springer, Berlin
Zhang ZQ, Liu WQ (2014) Geometric average Asian option pricing for uncertain financial market. J Uncertain Syst 8(4):317–320
Zhang ZQ, Gao R, Yang XF (2016) The stability of multifactor uncertain differential equation. J Intell Fuzzy Syst 30(6):3281–3290
Zhang ZQ, Liu WQ, Sheng YH (2016) Valuation of power option for uncertain financial market. Appl Math Comput 286:257–264
Zhang ZQ, Ralescu DA, Liu WQ (2016) Valuation of interest rate ceiling and floor in uncertain financial market. Fuzzy Optim Decis Mak 15(2):139–154
Zhang ZQ, Liu WQ, Zhang XD (2017) Valuation of convertible bond under uncertain mean-reverting stock model. J Ambient Intell Humaniz Comput 8(5):641–650
Zhang ZQ, Liu WQ, Ding JH (2018) Valuation of stock loan under uncertain environment. Soft Comput 22(17):5663–5669
Zhu Y (2010) Uncertain optimal control with application to a portfolio selection model. Cybern Syst 41(7):535–547
Acknowledgements
This work were supported by Doctoral Fund of Shanxi Datong University (No. 2016-B-03) and Program for Young Excellent Talents in UIBE (No. 18YQ06).
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Zhang, Z., Yang, X. Uncertain population model. Soft Comput 24, 2417–2423 (2020). https://doi.org/10.1007/s00500-018-03678-6
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DOI: https://doi.org/10.1007/s00500-018-03678-6