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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[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 xn+1=A+B/xn, Soft Comput., 6 (2002), 456--461. |
[10] | G. Papaschinopoulos and B. K. Papadopoulos, On the fuzzy difference equation xn+1=A+xn/xn−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 xn+1=A+B/xn, 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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