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A class of linear differential dynamical systems with fuzzy matrices |
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| Authors: | Jiuping Xu Zhigao Liao Juan J Nieto |
| Institution: | a Uncertainty Decision-Making Laboratory, School of Business and Administration, Sichuan University, Chengdu 610064, PR China b Management Department, Guangxi Technology University, Liuzhou 545006, PR China c Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Santiago de Compostela, 15782, Spain |
| Abstract: | This paper investigates the first order linear fuzzy differential dynamical systems with fuzzy matrices. We use a complex number representation of the α-level sets of the fuzzy system, and obtain the solution by employing such representation. It is applicable to practical computations and has also some implications for the theory of fuzzy differential equations. We then present some properties of the 2-dimensional dynamical systems and their phase portraits. Some examples are considered to show the richness of the theory and we can clearly see that new behaviors appear. We finally present some conclusions and new directions for further research in the area of fuzzy dynamical systems. |
| Keywords: | Fuzzy differential equation Fuzzy dynamical systems Fuzzy matrices |
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