Attractivity with asymptotic phase of local center manifolds and an application to one-parameter bifurcation for integral equations with infinite delay
For autonomous C 1 -smooth integral equations with infinite delay, exponential attractivity with asymptotic phase of the local center manifolds of the equilibrium 0, together with a reduction principle, is proved by means of a dynamical systems approach based on the variation-of-constants formula in...
Elmentve itt :
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| Dokumentumtípus: | Folyóirat |
| Megjelent: |
2025
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| Sorozat: | Electronic journal of qualitative theory of differential equations
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| Kulcsszavak: | Integrálegyenlet - végtelen késleltetésű, Bifurkáció |
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| doi: | 10.14232/ejqtde.2025.1.12 |
| Online Access: | http://acta.bibl.u-szeged.hu/88892 |
| Tartalmi kivonat: | For autonomous C 1 -smooth integral equations with infinite delay, exponential attractivity with asymptotic phase of the local center manifolds of the equilibrium 0, together with a reduction principle, is proved by means of a dynamical systems approach based on the variation-of-constants formula in the phase space established in [Funkcial. Ekvac. 55(2012), 479–520]. As its application to one-parameter family of integral equations, it is also shown that saddle-node and pitchfork bifurcations occur when the equilibrium 0 (the zero solution) of the linearized equation changes its stability properties. |
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| Terjedelem/Fizikai jellemzők: | 53 |
| ISSN: | 1417-3875 |