相关论文: Some Applications of the Method of Normal Fundamen…

The mathematical model of a real flexible elastic system with distributed and discrete parameters is considered. It is a partial differential equation with non-classical boundary conditions. Complexity of the boundary conditions results in…

We present a methodology for numerically integrating ordinary differential equations containing rapidly oscillatory terms. This challenge is distinct from that for differential equations which have rapidly oscillatory solutions: here the…

Neutrino oscillations are studied in the general framework of open quantum systems by means of extended dynamics that take into account possible dissipative effects. These new phenomena induce modifications in the neutrino oscillation…

We rigorously show that a class of systems of partial differential equations modeling wave bifurcations supports stationary equivariant bifurcation dynamics through deriving its full dynamics on the center manifold(s). A direct consequence…

Many combinatorial optimization problems can be mapped to finding the ground states of the corresponding Ising Hamiltonians. The physical systems that can solve optimization problems in this way, namely Ising machines, have been attracting…

A study of the non linear modes of a two degree of freedom mechanical system with bilateral elastic stop is considered. The issue related to the non-smoothness of the impact force is handled through a regularization technique. In order to…

Motivated by recent problems in mathematical cosmology, in which temporal averaging methods are applied in order to analyze the future asymptotics of models which exhibit oscillatory behavior, we provide a theorem concerning the large-time…

An understanding of the dynamics of differentially rotating systems is key to many areas of astrophysics. We investigate the oscillations of a simple system exhibiting differential rotation, and discuss issues concerning the role of…

A system obeying the harmonic oscillator equation of motion can be used as a force or proper acceleration sensor. In this short review we derive analytical expressions for the sensitivity of such sensors in a range of different situations,…

Networks of coupled phase oscillators are one of the most studied dynamical systems with numerous applications in physics, chemistry, biology, and engineering. Their behaviour is often characterized by the emergence of various partially…

For the study of highly nonlinear, conservative dynamic systems, finding special periodic solutions which can be seen as generalization of the well-known normal modes of linear systems is very attractive. However, the study of…

We describe an elementary method for bounding a one-dimensional oscillatory integral in terms of an associated non-oscillatory integral. The bounds obtained are efficient in an appropriate sense and behave well under perturbations of the…

Intractable phase dynamics often challenge our understanding of complex oscillatory systems, hindering the exploration of synchronisation, chaos, and emergent phenomena across diverse fields. We introduce a novel conceptual framework for…

We prove the existence of nonlinear normal modes for general systems of two coupled nonlinear oscillators. Facilitating the comparison principle for ordinary differential equations it is shown that there exist exact solutions representing a…

The increasing difficulty in continued development of digital electronic logic has led to a renewed interest in alternative approaches. Oscillatory computing is one such approach that leverages alternative physical systems and computation…

Optomechanical systems are known to exhibit a rich set of complex dynamical features including various types of chaotic behavior and multi-stability. Although this exotic behavior has attracted an intense research interest, the utilization…

This letter proposes an analytical approach to formulate the power system oscillation frequency under a large disturbance. A fact is revealed that the oscillation frequency is only the function of the oscillation amplitude when the system's…

In this manuscript, we discuss the use of describing functions as a systematic approach to the analysis and design of oscillators. Describing functions are traditionally used to study the stability of nonlinear control systems, and have…

Modelling stochastic systems has many important applications. Normal form coordinate transforms are a powerful way to untangle interesting long term macroscale dynamics from detailed microscale dynamics. We explore such coordinate…

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…