Related papers: Analyzing Oscillators using Describing Functions
We analyze how complicated a linear optical component has to be if it is to perform one of a range of functions. Specifically, we devise an approach to evaluating the number of real parameters that must be specified in the device design or…
This paper provides a first example of constructing Lyapunov functions in a class of piecewise linear systems with limit cycles. The method of construction helps analyze and control complex oscillating systems through novel geometric means.…
Determining functionals are tools to describe the finite dimensional long-term dynamics of infinite dimensional dynamical systems. There also exist several applications to infinite dimensional {\em random} dynamical systems. In these…
Description Logics (DLs) are a family of knowledge representation formalisms mainly characterised by constructors to build complex concepts and roles from atomic ones. Expressive role constructors are important in many applications, but can…
We investigate some types of composition operators, linear and not, and conditions for some spaces to be mapped into themselves and for the operators to satisfy some good properties.
We generalize our recent approach to reconstruction of phase dynamics of coupled oscillators from data [B. Kralemann et al., Phys. Rev. E, 77, 066205 (2008)] to cover the case of small networks of coupled periodic units. Starting from the…
In the presence of interactions the frequency of a simple harmonic oscillator deviates from the noninteracting one. Various methods can be used to compute the changes to the frequency perturbatively. Some of them resemble the methods used…
Relaxation oscillator-based circuits are widely used for interfacing various resistive and capacitive sensors. The electrical equivalent of most resistive and capacitive sensors is represented using a parallel combination of resistor and…
In this paper we review recent work on novel computing paradigms using coupled oscillatory dynamical systems. We explore systems of relaxation oscillators based on linear state transitioning devices, which switch between two discrete states…
The wide application of estimation techniques in system analysis enable us to best determine and understand the history of system states. This paper attempts to delineate the theory behind linear and non-linear estimation with a suitable…
Oscillatory systems arise in the different science fields. Complex mathematical formulations with differential equations have been proposed to model the dynamics of these systems. While they have the advantage of having a direct…
This article provides an overview of model predictive control (MPC) frameworks for dynamic operation of nonlinear constrained systems. Dynamic operation is often an integral part of the control objective, ranging from tracking of reference…
Static analyses overwhelmingly trade precision for soundness and automation. For this reason, their use-cases are restricted to situations where imprecision isn't prohibitive. In this paper, we propose and specify a static analysis that…
Kink oscillations in coronal loops have been extensively studied for their potential contributions to coronal heating and their role in plasma diagnostics through coronal seismology. A key focus is the strong damping of large-amplitude kink…
Logic is playing an increasingly important role in the engineering of real-time, hybrid, and cyber-physical systems, but mostly in the form of posterior verification and high-level analysis. The core methodology in the design of real-world…
Sustained oscillations observed in power systems can damage equipment, degrade the power quality and increase the risks of cascading blackouts. There are several mechanisms that can give rise to oscillations, each requiring different…
We study limit cycles of nonlinear oscillators described by the equation $\ddot x + \nu F(\dot x) + x =0$. Depending on the nonlinearity this equation may exhibit different number of limit cycles. We show that limit cycles correspond to…
Physical systems with symmetries are described by functions containing kinematical and dynamical parts. We consider the case when kinematical symmetries are described by a noncompact semisimple real Lie group $G$. Then separation of…
The diffusive behavior of a harmonic oscillator driven by a Mittag-Leffler noise is studied. Using Laplace analysis we derive exact expressions for the relaxation functions of the particle in terms of generalized Mittag-Leffler functions…
Adding explanations to recommender systems is said to have multiple benefits, such as increasing user trust or system transparency. Previous work from other application areas suggests that specific user characteristics impact the users'…