Abstract
In this paper, we propose the existence criterion of equilibrium point of fuzzy linear system x̃(k + 1) = Ã x̃(k) based on fuzzy arithmetic with identity constraint and fuzzy number expression based on structured element. Then we give a solving method of equilibrium point, propose the concept of generalized equilibrium point of fuzzy linear system, and finally, we use the example in macroeconomics to illustrate the necessity of using fuzzy arithmetic with identity constraint and the feasibility of our method.
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References
Tan, X.B.: Mathematical Methods for Economic theory. Shanghai Science and Technology Press, Shanghai (1963)
Blat, J., Brown, J.: Bifurcation of steady-state solutions in the predatorprey and competition systems. J. of Royal Society of Edinburgh 77, 21–34 (1984)
Korman, P., Leung, A.: On the existence and uniqueness of positive steady state in the Volterra-Lotka ecological models with diffusion Application Analysis, pp. 145–160 (1987)
Wu, J.H.: Coexistence states for cooperative model with diffusion. J. of Computers Mathematics Application 43, 1277–1290 (2002)
Xie, Q.J., Wu, J.H., Hei, L.: Coexistence of Nonnegative Steady-State Solutions for a Class of Reaction-Diffusion Equations. J. of Acta Mathematica since 22, 467–478 (2004)
Zhou, R.J., Deng, X.H., Tong, X.J.: Stable equilibrium point model of power system based on stability constraints. J. of Electric Power Automation Equipment 28(1), 12–16 (2008)
Li, J., Li, Y.L.: Local bifurcation and stability of steady state solutions of a reaction-diffusion systems. J. of Shaanxi Normal University (Natural Science Edition) 36(2), 15–18 (2008)
Liu, Q., Ma, Y.: Existence and Global Stability of Positive Equilibrium Point to a System of Differential Equations. J. of Mathematical Research and Exposition 27(4), 819–825 (2007)
Zhang, H.X., Gao, H.J.: Asymptotic Behavior for Constant Equilibria for Ginzburg-Landau Equation with Delay. J. of Nanjing Normal University (Natural Science Edition) 31(4), 14–20 (2008)
Zhou, Y.P.: Global Stability of Positive Equilibrium Point to a Competition Model in Chemical Reaction with Toxin. J. of College Mathematicae Applicatae Sinica 23(4), 437–446 (2008)
Miao, Y.S.: The Equilibrium Point in Fuzzy Economic Systems. J. of Fuzzy Systems and Mathematics 6(1), 9–14 (1992)
Zhu, K.P., Zhong, M.Y., Tang, B.Y.: Study on Algorithm for the Greatest Equilibrium State of Fuzzy Control Systems. J. of Fuzzy Systems and Mathematics 15(3), 80–83 (2001)
Guo, S.C., Liu, H.T.: Equality and Identity of Fuzzy Numbers and Fuzzy Arithmetic with Equality Constraints. J. of Fuzzy Systems and Mathematics 22(6), 76–82 (2008)
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Gao, Jb., Guo, Sz. (2010). A Solving Method of Fuzzy Linear System’s Equilibrium Point. In: Cao, By., Wang, Gj., Guo, Sz., Chen, Sl. (eds) Fuzzy Information and Engineering 2010. Advances in Intelligent and Soft Computing, vol 78. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14880-4_21
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DOI: https://doi.org/10.1007/978-3-642-14880-4_21
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-14879-8
Online ISBN: 978-3-642-14880-4
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