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Biyolojik, elektriksel ve mekaniksel osilatörler: senkronizasyon, kaos ve çatallanma

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2014
Akhmet, Marat
Kıvılcım, Ayşegül
In this project, the dynamics of differential equations that possess asymptotically stable equilibrium points or asymptotically stable limit cycles are investigated when they are perturbed chaotically. It is theoretically proved that the outputs are chaotic when the inputs are chaotic. The controllability of the obtained chaos is demonstrated. The chaos generation problem in cellular neural networks is considered and the formation of cyclic chaos in Hopfield neural networks is investigated. In our studies, chaos in the sense of Devaney and Li-Yorke as well as the one obtained through period-doubling cascade are utilized. Intermittency route to chaos, Shilnikov orbits and chaos appearance in Chua oscillators are investigated numerically. Besides, the presence of discontinuous limit cycle in Van der Pol equation with impacts on surfaces in the phase space is proved within the scope of the project. Our results are compared with the generalized synchronization concept and supported by simulations.