Browsing by Subject "Nonlinear Dynamics"

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Open Access
Comment on "modeling the electrical conduction in DNA nanowires: Charge transfer and lattice fluctuation theories"
(American Physical Society, 2016) Panahi, M.; Chitsazanmoghaddam, M.
In a recent paper [S. Behnia and S. Fathizadeh, Phys. Rev. E 91, 022719 (2015)10.1103/PhysRevE.91.022719] an analytical approach is proposed for the investigation of the conductivity properties of DNA. The authors use mean Lyapunov exponent methods as the backbone of their approach and try to interpret properties of the system based on its behavior. Their interpretation regarding the change in nature of the mean Lyapunov exponent at the denaturation temperatures and discussions of stability and instability based on the mean Lyapunov exponent method are questioned. Moreover there is misunderstanding between mean Lyapunov exponent and Lyapunov exponent. © 2016 American Physical Society.
Open Access
Essays on nonlinear dynamics in optimal growth models
(2014) Yüksel, Mustafa Kerem
Economic models with time delay have long been considered in economic theory. It is considered that delay forces the economic system into persistent cycles which can be interpreted as intrinsic crises of the capitalist economy. The e§ect of delay on economic dynamics is analyzed by Hopf bifurcation according to the recent developments in economics and mathematics. Hopf bifurcation depends on the existence of a pair of pure imaginary eigenvalues of the Jacobian matrix evaluated at the steady state. However, recent studies are inconsistent in a determinate way to decide whether the optimal growth model with investment lags admits persistent cycles or not. In the second chapter of this thesis, the author tries to sharpen the analysis of one sector optimal growth model with one control and one state variables and time delay. We Örstly give a brief outline of the mathematical history and ëknow-howíof delays in economic models, as well as its interpretation, and then, we further the analysis set of the model of Asea and Zak (1999) and try to introduce of a new technique for the exposition of the eigenvalues of the characteristic equation of these type of models in a generalized framework. In the third chapter we introduce a new technique (see Louisell, 2001) to the study of economic models with delays and incorporate this technique to evaluate the cycleinducing e§ects of capital dependent population growth in economic models with time delay. We employ the Solow-Kalecki framework and show that the presence of capital dependent population growth induces cycles. Other than the introduction of a new technique into the area of economics, one particular contribution of this chapter is that the results clearly shows that delay is not su¢ cient in inducing cycles even in the most simple economic models. In the forth chapter, we show that Hopf bifurcation may emerge in an overlapping generations resource economy through a feedback mechanism between population and resource availability. In overlapping generations resource economy models, the cycle inducing factor is mainly the nonlinearity of the regeneration of the resources. On the contrary, we assume linear regeneration and yet, endogenize the population growth rate. We show that the interaction between instantenous population growth and regeneration rate triggers persistent cycles in the economy. In the Öfth chapter, we employ a continuous delay structure in the process of recruitment in the population growth in an optimal growth model and hence obtain cyclic solutions. We exploit Erlangian process in the population growth mechanism. As far as we know, the incorporation of Erlangian process in optimal growth models is handled in this chapter for the Örst time in economic literature. Through this mechanism, not only the population is considered as a function of per capita capital, or in other words, population growth is endogenized, but also the current level of population growth is linked with those of older generations. We Önd out that the interaction between the e§ect of older generationsífertility choices and the accumulation of capital induces cyclic behaviour in the economy. The sixth and the last chapter concludes with future research agenda. Overall, the thesis considers the e§ects of delay and endogenized population on the economies of interest (Solow, overlapping generations, optimal growth model) economically and tries to introduce the existing methods and develop new ones to investigate the e§ects of delay and endogenized population on the eigenvalues of the Jacobians that the drive the economies of interest at their steady states.
Open Access
Parametric nonlinear lumped element model for circular CMUTs in collapsed mode
(2014) Aydoǧdu, E.; Ozgurluk, A.; Atalar, Abdullah; Köymen, Hayrettin
We present a parametric equivalent circuit model for a circular CMUT in collapsed mode. First, we calculate the collapsed membrane deflection, utilizing the exact electrical force distribution in the analytical formulation of membrane deflection. Then we develop a lumped element model of collapsed membrane operation. The radiation impedance for collapsed mode is also included in the model. The model is merged with the uncollapsed mode model to obtain a simulation tool that handles all CMUT behavior, in transmit or receive. Large- and small-signal operation of a single CMUT can be fully simulated for any excitation regime. The results are in good agreement with FEM simulations. © 2014 IEEE.