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A note on asymptotic equilibrium for fuzzy differential equations. (English) Zbl 1406.34004

Summary: The asymptotic equilibrium results for fuzzy differential systems \((GCP)x^\prime = f_1(t,x,y),y^\prime= f_2(t,x,y)\) are investigated, where \(f_1(t,x,y)\) satisfies the compactness-type and \(f_2(t,x,y)\) satisfies the dissipative-type conditions. It is worth mentioning that the uniformly continuous conditions of \(f(t,x,y)\) are removed in [S. Song et al., Comput. Math. Appl. 51, No. 9–10, 1483–1492 (2006; Zbl 1157.34002)]. That is to say, the results of Song et al. [loc. cit.] are extended. In addition, the global existence and asymptotic equilibrium results of fuzzy differential systems \((CP) x^\prime(t)=f(t,x),x(0)=x_0\) are obtained.

MSC:

34A07 Fuzzy ordinary differential equations
34C60 Qualitative investigation and simulation of ordinary differential equation models
34D05 Asymptotic properties of solutions to ordinary differential equations

Citations:

Zbl 1157.34002
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