Extension of the logistic equation with piecewise constant arguments and population dynamics

---

Tezin Türü: Yüksek Lisans

Tezin Yürütüldüğü Kurum: Orta Doğu Teknik Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, Türkiye

Tezin Onay Tarihi: 2006

Öğrenci: DERYA ALTINTAN

Danışman: MARAT AKHMET

Özet:

Population dynamics is the dominant branch of mathematical biology. The first model for population dynamics was developed by Thomas Malthus. A more complicated model was developed by Pierre François Verhulst and it is called the logistic equation. Our aim in this thesis is to extend the models using piecewise constant arguments and to find the conditions when the models have fixed points, periodic solutions and chaos with investigation of stability of periodic solutions.