The paper investigates Hopf bifurcations in a class of simple nonlinear systems, i.e., third order affine control systems described in terms of “quadratic plus cubic” normal forms and subject to linear state feedback control laws. By employing Harmonic Balance (HB) tools, the set of system parameters corresponding to supercritical and subcritical bifurcations is analytically determined. Also, a...

On the other hand, many modeling engineers still have some problems in understanding the basics of such nonlinear RF modeling. Applying a harmonic balance simulator like Agilent's ADS is a smart way to begin with some studies of the non-linear performance of devices and their corresponding model behavior, even when there are currently no measurement capabilities at hand in the modeling engineer...

Oscillatory chemical reactions often serve as a timing clock of cellular processes in living cells. The temporal dynamics of protein concentration levels is thus of great interest in biology. Here we propose a theoretical framework to analyze the frequency, phase and amplitude of oscillatory protein concentrations in gene regulatory networks with negative cyclic feedback. We first formulate the...

Thus we have, in a very limited field of research, briefly touched upon the relationship of the purely descriptive and experimental embryologist as to the methods of approach which each has taken in searching for the truth. The former points out the difficult barriers in the path of his progress. His judgment ofter later proves to be amazingly accurate in spite of the limitations of the methods...

In this paper we will study the non-linear oscillation of a conservative system having inertia and static non-linearities. By combining the linearization of the governing equation with the method of harmonic balance, we investigate analytical approximate solutions for the non-linear oscillations of the system. Unlike the classical harmonic balance method, linearization is performed prior to pro...

A time-domain harmonic balance method for the analysis of almost-periodic (multi-harmonics) flows is presented. This method relies on Fourier analysis to derive an efficient alternative to classical time marching schemes for such flows. It has recently received significant attention, especially in the turbomachinery field where the flow spectrum is essentially a combination of the blade passing...

CHRISTOFFERSEN, CARLOS ENRIQUE. State Variable Harmonic Balance Simulation of a Quasi-Optical Power Combining System. (Under the direction of Michael B. Steer.) A state variable implementation of harmonic balance circuit analysis is developed. The equations are formulated with the minimum number of unknowns starting from the modified nodal admittance matrix of the linear part of the circuit. Th...

Nonlinear energy sink (NES) refers to a typical passive vibration device connected linear or weakly nonlinear structures for absorption and mitigation. This study investigates the dynamics of 1-dof 2-dof NES with damping combined stiffness oscillator. For system NES, truncation failure frequency are revealed through bifurcation analysis using complex variable averaging method. The detuning inte...