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IUT 77142 Degree Master of Science Title The Kuramoto Model with Time Dependent Forcing Author Tahereh Malakoutikhah Supervisor F Shahbazi Assoc Prof Department Physics Date September 17 2013 Language Persian Abstract Synchronization is an adjustment of frequencies and phases of oscillation of group of oscillators due to interaction between the oscillating processes This phenomenon is observed a lot in nature This was the motivation for us to investigate the coupled oscillators under kuramoto model Living systems change with time However neither the original model nor its extensions have incorporated a fundamental property of living systems their inherent time variability Important characteristics of open systems can readily be missed by not accounting for the non equilibrium dynamics stemming from their time dependent parameters We introduce a generalization of the Kuramoto model by considerating the deterministically time varying parameters The natural frequencies of oscillators are influenced by an external time dependent force This external force can be considered as a periodic function like The coupling constant between oscillators can be considered a constant value for all of them or coupling constant for each oscillator can be normalized to the number of interactions that each oscillator has with other oscillators We investigate the generalization of the Kuramoto model with unnormalized coupling constant as well as the model with normalized coupling constant by the number of interactions The behavior of the system are identical in both situations but the time of reaching to stationary state is different Furthermore We consider a normal distribution or bimodal distribution for natural frequencies and investigate the model when amplitude of applied force has bimodal or Gaussian distribution In this situation we observe a new dynamics of the collective rhythms in a way that all of the oscillators move in a synchronized way at a moment and at the next instant they move totally in an asynchronized way Investigating the behavior of different networks under this model shows that the amplitude and period of order parameter decreases when the frequency of applied force increases The behavior of small world network is often different from the other networks We observe a resonance behavior when the natural frequencies have normal distribution and the amplitude of applied force has bimodal distribution In this situation when the frequency of applied force increases the amplitude of order parameter increases and after that it decreases We investigate the influence of applying the white noise on all of oscillators in both situation in which the coupling is unnormalized or normalized In either cases the order parameter of system is increased for a strength of white noise and we have stochastic synchronization The strength of the white noise for the model with normalized coupling constant is less than the strength of it for the model with unnormalized coupling constant Furthermore we investigate the influence of applying the white noise on defects of small world network When we apply white noise on the defects of network for some strengths of white noise the order parameter approaches to one and the defects of network are vanished Keywords the Kuramoto model synchronization order parameter small world network random network scale free network PDF created with pdfFactory trial version www pdffactory com

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مدل كوراموتو با نيروي وابسته به زمان

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