The harmonic balance (HB) principle is a powerful and convenient tool for finding periodic solutions in nonlinear systems. In the present paper, this principle is extended to transient processes in systems with one single-valued odd-symmetric nonlinearity and linear plant not having zeros in the transfer function, and named the dynamic HB. Based on the dynamic HB, first the equations for the am...

Krylov subspace techniques in harmonic balance simulations become increasingly ineffective when applied to strongly nonlinear circuits. This limitation is particularly important in the simulation if the circu it has components being operated in a very nonlinear region. Ev en if the circuit contains only a few very nonlinear components, Krylov methods using standard preconditioners can become in...

Here we analyze properties of an equation that we previously proposed to model the dynamics of unstable detonation waves [A. R. Kasimov, L. M. Faria, and R. R. Rosales, Model for shock wave chaos, Phys. Rev. Lett., 110 (2013), 104104]. The equation is ut+ 1 2 ( u2 − uu 0−, t x = f ( x, u ( 0−, t )) , x ≤ 0, t > 0. It describes a detonation shock at x = 0 with the reaction zone in x < 0. We inve...

A new approach to parallelizing harmonic balance simulation is presented. The technique leverages circuit substructure to expose potential parallelism in the form of a directed, acyclic graph (dag) of computations. This dag is then allocated and scheduled using various linear clustering techniques. The result is a highly scalable and efcient approach to harmonic balance simulation. Two large ex...

In the context of the future new definition of the mass unit, kg, a promising route to link the mass unit to a fundamental constant, the Planck constant h, is represented by the watt balance experiment. Since a number of years, the Federal Institute of Metrology is active in this field and published a first result with its Mark I experiment in 2011. To reach the target uncertainty of 2 parts in...

The concept of the dissipative soliton has received wide recognition in optics (physics in general), biology and medicine [Akhmediev & Ankiewicz, 2005, 2008]. This concept allows many diverse phenomena in nature to be understood and studied in a simple and systematic way. It represents a unifying notion in science, since it stresses common features in a variety of complicated behaviors of self-...

We consider oscillators consisting of a reactance circuit and a negative resistor. They may happen to have multi-mode oscillations around the anti-resonant frequencies of the reactance circuit. This kind of oscillators can be easily synthesized by setting the resonant and antiresonant frequencies of the reactance circuits. However, it is not easy to analyze the oscillation phenomena, because th...

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...