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Stability criteria of the Vlasov equation and quasi-stationary states of the HMF model

✍ Scribed by Yoshiyuki Y. Yamaguchi; Julien Barré; Freddy Bouchet; Thierry Dauxois; Stefano Ruffo

Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
877 KB
Volume
337
Category
Article
ISSN
0378-4371

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On the stability of the stationary state
On the stability of the stationary state of a population growth equation with time-lag
✍ K. P. Hadeler 📂 Article 📅 1976 🏛 Springer 🌐 English ⚖ 176 KB

If in the Verhulst equation for population growth the reproduction factor depends on the history then the equilibrium may become unstable and oscillations and even non-constant periodic solutions may occur. It is shown that the equilibrium is unstable if the reproduction factor at time t is, up to a