### Mathematical Biosciences and Engineering

2019, Issue 3: 1471-1488. doi: 10.3934/mbe.2019071
Research article

# On discrete time Beverton-Holt population model with fuzzy environment

• Received: 05 November 2018 Accepted: 25 January 2019 Published: 21 February 2019
• In this work, dynamical behaviors of discrete time Beverton-Holt population model with fuzzy parameters are studied. It provides a flexible model to fit population data. For three different fuzzy parameters and fuzzy initial conditions, according to a generalization of division (g-division) of fuzzy number, it can represent dynamical behaviors including boundedness, global asymptotical stability and persistence of positive solution. Finally, two examples are given to demonstrate the effectiveness of the results obtained.

Citation: Qianhong Zhang, Fubiao Lin, Xiaoying Zhong. On discrete time Beverton-Holt population model with fuzzy environment[J]. Mathematical Biosciences and Engineering, 2019, 16(3): 1471-1488. doi: 10.3934/mbe.2019071

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• In this work, dynamical behaviors of discrete time Beverton-Holt population model with fuzzy parameters are studied. It provides a flexible model to fit population data. For three different fuzzy parameters and fuzzy initial conditions, according to a generalization of division (g-division) of fuzzy number, it can represent dynamical behaviors including boundedness, global asymptotical stability and persistence of positive solution. Finally, two examples are given to demonstrate the effectiveness of the results obtained.

 [1] M. Kot, Elements of Mathematical Ecology, Cambridge University Press, New York, 2001. [2] R. Beverton and S. Holt, On the dynamics of exploited fish populations, Fish. Invest. Ser 2, 19 (1957), 1–533. [3] M. D. L. Sen, The generalized Beverton-Holt equation and the control of populations, Appl. Math. Model., 32 (2008), 2312–2328. [4] M. D. L. Sen and S. Alonso-Quesada, Control issues for the Beverton-Holt equation in ecology by locally monitoring the environment carrying capacity: Nonadaptive and adaptive cases, Appl. Math. Comput., 215 (2009), 2616–2633. [5] M. Bohner and S. Streipert, Optimal harvesting policy for the Beverton-Holt model, Math. Biosci. Eng., 13 (2016), 673–695. [6] L. A. Zadeh, Fuzzy set, Inf. Control, 8 (1965), 338–353. [7] E. Y. Deeba, A. De Korvin and E. L. Koh, A fuzzy difference equation with an application, J. Differ. Equ. Appl., 2 (1996), 365–374. [8] E. Y. Deeba and A. De Korvin, Analysis by fuzzy difference equations of a model of CO2 level in the blood, Appl. Math. Lett., 12 (1999), 33–40. [9] G. Papaschinopoulos and B. K. Papadopoulos, On the fuzzy difference equation $x_{n+1} = A + B/x_n$, Soft Comput., 6 (2002), 456--461. [10] G. Papaschinopoulos and B. K. Papadopoulos, On the fuzzy difference equation $x_{n+1}=A+x_n/x_{n-m}$, Fuzzy Set. Syst., 129 (2002), 73--81. [11] G. Stefanidou, G. Papaschinopoulos and C. J. Schinas, On an exponential-type fuzzy difference equation, Adv. Differ. Equ., 2010 (2010), 1–19. [12] Q. Din, Asymptotic behavior of a second order fuzzy rational difference equations, J. Discrete Math., 2015 (2015), 1–7. [13] R. Memarbashi and A. Ghasemabadi, Fuzzy difference equations of volterra type, Int. J. Nonlinear Anal. Appl., 4 (2013), 74–78. [14] K. A. Chrysafis, B. K. Papadopoulos and G. papaschinopoulos, On the fuzzy difference equations of finance, Fuzzy Set. Syst., 159 (2008), 3259–3270. [15] Q. Zhang, L. Yang and D. Liao, Behaviour of solutions of to a fuzzy nonlinear difference equation, Iranian J. Fuzzy Syst., 9 (2012), 1–12. [16] Q. Zhang, L. Yang and D. Liao, On first order fuzzy riccati difference equation, Inform. Sciences, 270 (2014), 226–236. [17] Q. Zhang, J. Liu and Z. Luo, Dynamical behaviour of a third-order rational fuzzy difference equation, Adv. Differ. Equ., 2015 (2015). [18] S. P. Mondal, D. K. Vishwakarma and A. K. Saha, Solution of second order linear fuzzy difference equation by Lagranges multiplier method, J. Soft Comput. Appl., 1 (2016), 11–27. [19] Z. Alijani and F. Tchier, On the fuzzy difference equation of higher order, J. Comput. Complex. Appl., 3 (2017), 44–49. [20] A. Khastan, Fuzzy Logistic difference equation, Iranian J. Fuzzy Syst., (2017), In Press. [21] C. Wang, X. Su, P. Liu, et al., On the dynamics of a five-order fuzzy difference equation, J. Nonlinear Sci. Appl., 10 (2017), 3303–3319. [22] A. Khastan and Z. Alijani, On the new solutions to the fuzzy difference equation $x_{n+1} = A + B/x_n$, Fuzzy Set. Syst., (2018), In Press. [23] A. Khastan, New solutions for first order linear fuzzy difference equations, J. Comput. Appl. Math., 312 (2017), 156–166. [24] D. Dubois and H. Prade, Possibility theory: an approach to computerized processing of uncertainty, Plenum Publishing Corporation, New York, 1998. [25] L. Stefanini, A generalization of Hukuhara difference and division for interval and fuzzy arithmetic, Fuzzy Set. Sys., 161 (2010), 1564–1584. [26] V. L. Kocic and G. Ladas, Global behavior of nonlinear difference equations of higher order with application, Kluwer Academic Publishers, Dordrecht, 1993. [27] M. R. S. Kulenonvic and G. Ladas, Dynamics of second order rational difference equations with open problems and conjectures, Chapaman & Hall/CRC, Boca Raton, 2002.
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