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 |
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