Global stability for the delayed logistic map

Abstract

First, I would like to express my sincere gratitude to my supervisor Tibor Krisztin for his valuable advice, for proposing interesting problems and for his support during my whole research.I would like to thank László Hatvani, supervisor of my bachelor's and master's thesis, for introducing me to the mysteries of dynamical system. I am also grateful to everyone in the Bolyai Institute -to my teachers and to my colleagues who made my university years memorable.I would like to express how lucky I am that I had wonderful teachers even before university, who made me love math and taught me that hard work bears fruit. I would like to emphasize my thanks to my elementary school teacher Ilona Fazekas and my high school teacher Tibor Nagy.Last, but not least, I also owe much gratitude to my family, especially my wife Evelin, my parents and my sister for their everlasting support and trust in me and my work.Without them this thesis would not have been written. the logistic map would also be interesting for larger delay, i.e., d > 2. We believe that the analytical part could be extended using only natural modications. However, the computer-aided part can be critical in these cases, since the increasing dimension causes an exponentially growing graph.It also would be interesting to prove the existence of the unique invariant closed curve around the nontrivial xed point for parameter values larger than the critical value.However, this question is substantially dierent from the one studied in this thesis.