Corresponding Banach spaces on time scales

Ruffing, Andreas; Simon, Moritz

doi:10.1016/j.cam.2004.09.047

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Definition 7 (Bohner and Peterson1

Introduction1

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Cited by 9 publications

(2 citation statements)

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“…Lemma 10 (contraction mapping principle [17]). If Ω is a closed subset of a Banach space and F : Ω → Ω is a contraction, then F has a unique fixed point in Ω.…”

Section: Definition 7 (Bohner and Petersonmentioning

confidence: 99%

Exponential Stability of Periodic Solution to Wilson-Cowan Networks with Time-Varying Delays on Time Scales

Cai

Bin

2014

Advances in Artificial Neural Systems

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We present stability analysis of delayed Wilson-Cowan networks on time scales. By applying the theory of calculus on time scales, the contraction mapping principle, and Lyapunov functional, new sufficient conditions are obtained to ensure the existence and exponential stability of periodic solution to the considered system. The obtained results are general and can be applied to discrete-time or continuous-time Wilson-Cowan networks.

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“…Lemma 10 (contraction mapping principle [17]). If Ω is a closed subset of a Banach space and F : Ω → Ω is a contraction, then F has a unique fixed point in Ω.…”

Section: Definition 7 (Bohner and Petersonmentioning

confidence: 99%

Exponential Stability of Periodic Solution to Wilson-Cowan Networks with Time-Varying Delays on Time Scales

Cai

Bin

2014

Advances in Artificial Neural Systems

View full text Add to dashboard Cite

show abstract

“…In [23], the sufficient conditions for the strict stability of dynamical systems on the time scale were given. Work [19] gave a generalization of the notions of Banach and Hilbert spaces of functions, as well as some examples illustrating a structure of appropriate spaces. In [7], some theorems on the practical stability of dynamical systems on the time scale were obtained with the help of differential inequalities.…”

Section: Introductionmentioning

confidence: 99%