一阶非线性模糊差分方程动力学行为研究
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摘要
利用模糊数广义除法,讨论一阶非线性模糊差分方程■,正解的存在性、唯一性以及稳定性,其中(x_n)是正模糊数数列,M,A,B是正模糊数,进一步通过数值例子,以验证结论的有效性。
In this paper, using the g-divsion of fuzzy numbers, we study the existence, the bounded and the asymptotic behavior of the positive solutions of the first order nonlinear fuzzy difference equation, ■, where(x_n) is a sequence of positive fuzzy numbers, M,A,B and initial value x_0 are positive fuzzy numbers. Finally, a numerical simulation example is given to verify the validity of the results.
In this paper, using the g-divsion of fuzzy numbers, we study the existence, the bounded and the asymptotic behavior of the positive solutions of the first order nonlinear fuzzy difference equation, ■, where(x_n) is a sequence of positive fuzzy numbers, M,A,B and initial value x_0 are positive fuzzy numbers. Finally, a numerical simulation example is given to verify the validity of the results.
引文
[1] Papaschinopoulos G,Schina C J.On a system of nonlinear difference equations[J].Journal of Mathematical Analysis and Applications,1998,219:415～426.
[2] Kocic V,Ladas G.Global behaviour of nonlinear difference equations of higher order with applications[M].Dordrecht:Kluwer Academic,1993.
[3] Liz E.A global picture of the Gamma-Ricker map:A flexible discrete-time model with factors of positive and negative densities dependence[J].Bulletin of Mathematical Biology,2018,80(2):417～434.
[4] Stevo S.Solution to the solvability problem for a class of product-type systems of difference equations[J].Advances in Difference Equations,2017,151:1～24.
[5] Din Q,Donche V.Global character of a host-parasite model[J].Chaos,Solitons and Fractals,2013,54(1):1～7.
[6] 张千宏,刘璟忠.论一阶模糊差分方程xn+1=Axn+B[J].模糊系统与数学,2009,23(4):74～79.
[7] Zhang Q H,Luo Z G,Liu J Z.Dynamical behavior of second-order rational fuzzy difference equation[J].International Journal of Dynamical Systems and Differential Equations,2015,5(4):336～353.
[8] Papaschinopoulos G,Schina B K.On the fuzzy difference equation .Soft Computing,2002,6:456～461.
[9] Zhang Q H,Liu J Z,Luo Z G.Dynamical behavior of a third-order rational fuzzy difference equation[J].Advance in Difference Equations,2015,108:1～18.
[10] Zhang Q H,Yang L H,Liao D X.On first order fuzzy Riccati difference equation[J].Information Sciences,2014,270:226～234.
[11] Wu C,Zhang B.Embedding problem of no compact fuzzy number space E[J].Fuzzy Sets and Systems,1999,105:165～169.
[12] Stefanini L.A generalization of Hukuhara difference and division for interval and fuzzy arithmetic[J].Fuzzy Sets and Systems,2010,161:1564～1584.
[13] Khastan A,Alijiani Z.On the new solutions to the fuzzy difference equation .Fuzzy Sets and Systems,2019,358(1):64～83.
[14] Papaschinopoulos G,Stefanidou G.Boundedness and asymptotic behavior of the solutions of a fuzzy difference equation[J].Fuzzy Sets and Systems,2003,140:523～539.
[15] Stefanidou G,Papaschinopoulos G.Behavior of the positive solutions of fuzzy max-difference equations[J].Advances in Difference Equations,2005,2:153～172.
[16] Stefanidou G,Papaschinopoulos G,Schinas C J.On an exponential-type fuzzy difference equation[J].Advances in Difference Equations,2010,2010:doi:10.1155/2010/196920.
[17] He Q,Tao C,Sun T,Liu X,Su D.Periodicity of the positive solutions of a fuzzy max-difference equation[J].Abstract and Applied Analysis,2014,2014,Article ID 760247,4 pages.
[2] Kocic V,Ladas G.Global behaviour of nonlinear difference equations of higher order with applications[M].Dordrecht:Kluwer Academic,1993.
[3] Liz E.A global picture of the Gamma-Ricker map:A flexible discrete-time model with factors of positive and negative densities dependence[J].Bulletin of Mathematical Biology,2018,80(2):417～434.
[4] Stevo S.Solution to the solvability problem for a class of product-type systems of difference equations[J].Advances in Difference Equations,2017,151:1～24.
[5] Din Q,Donche V.Global character of a host-parasite model[J].Chaos,Solitons and Fractals,2013,54(1):1～7.
[6] 张千宏,刘璟忠.论一阶模糊差分方程xn+1=Axn+B[J].模糊系统与数学,2009,23(4):74～79.
[7] Zhang Q H,Luo Z G,Liu J Z.Dynamical behavior of second-order rational fuzzy difference equation[J].International Journal of Dynamical Systems and Differential Equations,2015,5(4):336～353.
[8] Papaschinopoulos G,Schina B K.On the fuzzy difference equation .Soft Computing,2002,6:456～461.
[9] Zhang Q H,Liu J Z,Luo Z G.Dynamical behavior of a third-order rational fuzzy difference equation[J].Advance in Difference Equations,2015,108:1～18.
[10] Zhang Q H,Yang L H,Liao D X.On first order fuzzy Riccati difference equation[J].Information Sciences,2014,270:226～234.
[11] Wu C,Zhang B.Embedding problem of no compact fuzzy number space E[J].Fuzzy Sets and Systems,1999,105:165～169.
[12] Stefanini L.A generalization of Hukuhara difference and division for interval and fuzzy arithmetic[J].Fuzzy Sets and Systems,2010,161:1564～1584.
[13] Khastan A,Alijiani Z.On the new solutions to the fuzzy difference equation .Fuzzy Sets and Systems,2019,358(1):64～83.
[14] Papaschinopoulos G,Stefanidou G.Boundedness and asymptotic behavior of the solutions of a fuzzy difference equation[J].Fuzzy Sets and Systems,2003,140:523～539.
[15] Stefanidou G,Papaschinopoulos G.Behavior of the positive solutions of fuzzy max-difference equations[J].Advances in Difference Equations,2005,2:153～172.
[16] Stefanidou G,Papaschinopoulos G,Schinas C J.On an exponential-type fuzzy difference equation[J].Advances in Difference Equations,2010,2010:doi:10.1155/2010/196920.
[17] He Q,Tao C,Sun T,Liu X,Su D.Periodicity of the positive solutions of a fuzzy max-difference equation[J].Abstract and Applied Analysis,2014,2014,Article ID 760247,4 pages.