Vol. 5, No. 4 (2016): Regular Issue

Renewable resources such as atmospheric wind speed and global horizontal irradiance, possess huge fluctuations over a large range of spatial and temporal scales, indicating their nonlinear and nonstationary properties. In this study, the multiple scale dynamics and the correlations between simultaneous time series are analyzed using EMD (Empirical Mode Decomposition) based methods, particularly appropriate for such time series. We consider simultaneous wind speed-global horizontal irradiance measurements, sampled at 1 hour over a period of three years, from 2010 to 2013, at Guadeloupean Archipelago (French West Indies) located at 16°15'N latitude and 60°30'W longitude. After EMD decomposition of both time series, power laws are observed in the Fourier and Hilbert spaces over a broad range of frequencies. Furthermore, we investigate their local correlations using the Time Dependent Intrinsic Correlation method (TDIC). The time evolution and the scale dependence of their correlation are determined at different time scales and for different intrinsic modes functions. The estimation of TDIC have highlighted strong correlations for all the time scales, particularly strong negative correlations between both time series for mean periods 2h≤Tm<273 days indicating a complementarity between wind speed and global horizontal irradiance for these time scales.

This work is devoted to investigation of nonlinear electric circuit—the resonance scheme with nonlinear reactive element. The role of this non-linearity plays the saturation of magnetic transformed coupling. The stationary mode in this scheme is supported by generator of alternating current. The idea of work of parametron is an opportunity of two stationary modes of current corresponded to borders of the main zone of parametrical resonance. These modes are used as binary logical states with high-frequency ability of switching. The efficiency of this scheme increases with growth of frequency and simultaneously decreasing of scale. The aim of this article is a summarizing of the method of study for scheme of this type for this and some analogous devices.

This paper describes a nonlinear theory to describe oscillations of two liquid layers formed in a rectangular tank. Nonlinear equations based on the variational principle and the Galerkin method are used, which are written in a form of direct expanding in eigenmodes. Analysis using the equations is described under the experimental conditions reported in a previous study. Both the experiment and the analysis demonstrate a “peculiar oscillation” in which the interface of the two liquids oscillates at 1/5 to 1/7 of the excitation frequency in a particular excitation frequency range. By observing the nonlinear force time series, four eigenmodes are identified to be mainly relevant to the oscillation. An amplitude equation analysis was applied to the four relevant eigenmodes. It was found that this “peculiar oscillation” is one of summed and differential harmonic oscillations (combination oscillation) in which one asymmetric and one symmetric eigenmode excite each other through the mediation of other two asymmetric eigenmodes.

In this work the energy harvesting performance of a piezoelectric curved energy generator (THUNDER) is studied via experimental and analytical methods. The analytical model of the THUNDER is created based on the linear mechanical electrical constitutive law of the piezoelectric material, the linear elastic constitutive law of the substrate, and the Euler-Bernoulli beam theory. With these linear modal functions, the Rayleigh-Ritz approach was used to then obtain the reduced mechanical electrical coupled modulation equations. With above analytical model, two types of energy harvest circuit are proposed and compared: 1) directly charging mode at low level excitation, and 2) memory stored optimal duty cycle step-down converter mode at high level excitation. The value of the optimal duty cycle is determined based on the characteristics of the vibration signals of the ambient vibration source. To reduce the energy consumption of the microcontroller, the optimum duty cycle values are stored in the microprocessor instead of doing onsite computing during energy harvesting process. For the purpose of designing a low power cost mechanical switch to control the operation of both modes, the threshold voltage between these two operation modes is converted into threshold displacement.

In this paper, stability analysis of the nonlinear time-delayed Sprott system is made by applying a small perturbation near the critical point. Next, we will discuss a scheme for delay synchronization. To achieve our claim, we will make the chaos synchronization between the coupled Sprott system with delay parameters. Here, we will discuss five distinct cases. Numerical simulation is done to verify our claim.

This paper is devoted to obtain the global existence and blow up of solutions for two species chemotaxis system by the ratio of two solutions method. Our main concern is to show that the blow up properties of solutions depend only on the first eigenvalue.

This work concerns the dynamics of nonlinear systems that are subjected to delayed self-feedback. Perturbation methods applied to such systems give rise to slow flows which characteristically contain delayed variables. We consider two approaches to analyzing Hopf bifurcations in such slow flows. In one approach, which we refer to as approach I, we follow many researchers in replacing the delayed variables in the slow flow with non-delayed variables, thereby reducing the DDE slow flow to an ODE. In a second approach, which we refer to as approach II, we keep the delayed variables in the slow flow. By comparing these two approaches we are able to assess the accuracy of making the simplifying assumption which replaces the DDE slow flow by an ODE. We apply this comparison to two examples, Duffing and van der Pol equations with self-feedback.

This paper investigates the solution of fractional dynamical systems with the inverse operator method and Mittag-Leffler function. Controllability of linear fractional dynamical systems is studied by obtaining the Grammian operator. Sufficient conditions for both nonlinear and integrodifferential systems are established by the contraction principle. Some examples are provided to illustrate the theory.

The strongly nonlinear van der Pol oscillator represents a special challenge, which has prevented many methods from obtaining the closed-form solutions of the steady-state probability density functions (PDFs) in the literature. In this paper, we apply our recently developed method called the iterative method of weighted residue to analytically construct steady-state PDFs of the van der Pol oscillator under external Gaussian white noise excitation. The steady-state PDF is assumed to be an exponential function of polynomials in the state variables. The iterative method of weighted residue is used to compute the PDF. The iterative procedure that makes use of the obtained closed-form solutions of steady-state PDFs as the weighting function for the method improves the accuracy of the solution and the convergence of the solution process. The closed-form steady-state PDFs of strongly nonlinear van der Pol oscillator are presented in this paper, which were not available in the literature before, and are compared with those from the Monte Carlo simulations. The analytical and simulation results are in excellent agreement over a wide range of damping coefficients.