Multiple Mittag-Leffler stability and locally asymptotical ω-periodicity for fractional-order neural networks

Wan, Liguang; Wu, Ailong

doi:10.1016/j.neucom.2018.07.023

Cited by 17 publications

(15 citation statements)

References 21 publications

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“…Remark 5. Comparing with [14], our model with nonautonomous arguments and impulses is more complicated, and the previous results do not work in this case. Therefore, our results are new.…”

Section: Simulationsmentioning

confidence: 71%

“…Compared with the results on Mittag-Leffler multistability of autonomous FONNs [14], our asymptotic stability for the nonautonomous FONNs with impulses is more realistic. Besides, because of the discontinuity of z i (τ ), the method used in [14] cannot be directly utilized in this model. Therefore, our results are new.…”

Section: Asymptotic Multistability and Local S-asymptotic ω-Periodicitymentioning

confidence: 81%

“…From ( [14,34], the system discussed in this paper involves impulses, in which the state functions z i (τ ) are discontinuous in [τ 0 , ∞). Therefore, the method used for the positive invariant sets in [14] cannot be used up directly to this paper. The conditions‫א‬ i (τ, s…”

Section: The Invariant Sets and Boundednessmentioning

confidence: 99%

“…τ 0 of invariant sets for the FONNs with impulses and nonautonomous parameters are dual functions, which are more complicated than those with autonomous parameters, such as in [14].…”

Section: The Invariant Sets and Boundednessmentioning

confidence: 99%

“…The global SAP was considered by Chen for nonautonomous FONNs in [12] and for the nonautonomous FONNs with time-varying delays in [13]. Wan and Wu [14] discussed local SAP for the FONNs. However, they did not consider impulsive effects.…”

Section: Introductionmentioning

confidence: 99%

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Asymptotic multistability and local S-asymptotic ω-periodicity for the nonautonomous fractional-order neural networks with impulses

Kao

2020

Sci. China Inf. Sci.

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This paper focuses on the investigation of asymptotic multistability and on local S-asymptotic ω-periodicity for nonautonomous fractional-order neural networks (FONNs) with impulses. Several criteria on the existence, uniqueness, and invariant sets of nonautonomous FONNs with impulses are derived by constructing convergent sequences and comparison principles, respectively. In addition, using the Lyapunov direct method, some novel conditions of boundedness and local asymptotic stability of the FONNs discussed are obtained. Also, the sufficient conditions for local S-asymptotic ω-periodicities of the system are presented. Finally, a discussion using two examples verifies the validity of our findings, which imply that global asymptotic stability is a special case of asymptotic multistability.

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“…Remark 5. Comparing with [14], our model with nonautonomous arguments and impulses is more complicated, and the previous results do not work in this case. Therefore, our results are new.…”

Section: Simulationsmentioning

confidence: 71%

Section: Asymptotic Multistability and Local S-asymptotic ω-Periodicitymentioning

confidence: 81%

Section: The Invariant Sets and Boundednessmentioning

confidence: 99%

“…τ 0 of invariant sets for the FONNs with impulses and nonautonomous parameters are dual functions, which are more complicated than those with autonomous parameters, such as in [14].…”

Section: The Invariant Sets and Boundednessmentioning

confidence: 99%