Akademik Veri Yönetim Sistemi
Tezin Türü: Doktora
Tezin Yürütüldüğü Kurum: Orta Doğu Teknik Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, Türkiye
Tezin Onay Tarihi: 2013
Öğrenci: MEHMET ONUR FEN
Danışman: MARAT AKHMET
Özet:The main objective of this thesis is to develop a new method for chaos generation through the input/output mechanism on the basis of differential and discrete equations. In the thesis, this method is applied to various models in mechanics, electronics, meteorology and neural networks. Chaotic sets of continuous functions as well as the concepts of the generator and replicator of chaos are introduced. Inputs in the form of both continuous and piecewise continuous functions are applied to arbitrarily high dimensional systems with stable equilibrium points, and it is rigorously proven that the chaos type of the inputs is the same as for the outputs. Our theoretical results are based on the chaos in the sense of Devaney, Li-Yorke and the one obtained through period-doubling cascade. Besides, replication of Shil’nikov orbits, intermittency and the form of the bifurcation diagrams are investigated in the discussion form. It is shown that the usage of chaotic external inputs makes the dynamics of shunting inhibitory cellular neural networks exhibit chaotic motions. Moreover, the presence of chaos in the dynamics of the Duffing oscillator perturbed with a relay function is demonstrated. Models, in which the Lorenz system, shunting inhibitory cellular neural networks and Duffing oscillators are utilized as generators, are considered. Extension of chaos in open chains of Chua circuits and quasiperiodic motions as a possible skeleton of a chaotic attractor are also discussed. The controllability of the replicated chaos is theoretically proven and actualized by means of the OGY and Pyragas control methods.