Addendum to: “Attractivity, multistability, and bifurcation in delayed Hopfield’s model with non-monotonic feedback”. (English) Zbl 1291.34122
From the text: In our recent paper [ibid. 255, No. 11, 4244–4266 (2013; Zbl 1291.34121)], we developed some criteria of global attraction for general systems of delay differential equations based on a link with a finite-dimensional discrete dynamical system. In this note, we give an example showing the necessity of the key assumption in our main result. For convenience of the reader, we recall its statement.
MSC:
| 34K25 | Asymptotic theory of functional-differential equations |
| 39A10 | Additive difference equations |
Citations:
Zbl 1291.34121References:
| [1] | Ivanov, A. F.; Sharkovsky, A. N., Oscillations in singularly perturbed delay equations, Dynam. Report. Expositions Dynam. Systems (N. S.), 1, 164-224 (1992) · Zbl 0755.34065 |
| [2] | Liz, E.; Ruiz-Herrera, A., Attractivity, multistability, and bifurcation in delayed Hopfield’s model with non-monotonic feedback, J. Differential Equations, 255, 4244-4266 (2013) · Zbl 1291.34121 |
| [3] | Mallet-Paret, J.; Nussbaum, R., Global continuation and asymptotic behaviour for periodic solutions of a differential-delay equation, Ann. Mat. Pura Appl., 145, 33-128 (1986) · Zbl 0617.34071 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
