Related papers: Dynamics of a generalized Rayleigh system
We consider a dynamical system subjected to weak but adiabatically slow fluctuations of external origin. Based on the ``adiabatic following'' approximation we carry out an expansion in \alpha/|\mu|, where \alpha is the strength of…
We study the properties and stability of networks with arbitrary Laplacian coupling. Classic approaches to studying networked systems require unrealistic assumptions, including homogeneous node dynamics, one-dimensional and undirected…
The patch dynamics scheme in equation-free multiscale modelling can efficiently predict the macroscopic behaviours by simulating the microscale problem in a fraction of the space-time domain. The patch dynamics schemes developed so far, are…
A simple discontinuous map is proposed as a generic model for nonlinear dynamical systems. The orbit of the map admits exact solutions for wide regions in parameter space and the method employed (digit manipulation) allows the mathematical…
A new formulation of physical thermal models for variable plug flow through a pipe is proposed. The derived model is based on a commonly used one-dimensional distributed parameter model, which explicitly takes into account the heat capacity…
A comparative study of the Homotopy Analysis method and an improved Renormalization Group method is presented in the context of the Rayleigh and the Van der Pol equations. Efficient approximate formulae as functions of the nonlinearity…
Hybrid dynamical systems characterized by discrete switching of smooth dynamics have been used to model various rhythmic phenomena. However, the phase reduction theory, a fundamental framework for analyzing the synchronization of…
Stability of linear systems with uncertain bounded time-varying delays is studied under assumption that the nominal delay values are not equal to zero. An input-output approach to stability of such systems is known to be based on the bound…
Let C be a projective Gorenstein curve over an algebraically closed field of characteristic 0. A generalized linear system on C is a pair (I,f) consisting of a torsion-free, rank-1 sheaf I on C and a map of vector spaces f to the space of…
In this paper some new tools for the study of evolution problems in the framework of Young measures are introduced. A suitable notion of time-dependent system of generalized Young measures is defined, which allows to extend the classical…
In this work we find a sequence of functions at which the Pearcey function is identically zero. The sequence of functions can be expressed in terms of a second order non-linear ODE, which happens to be the Rayleigh-type. As a byproduct of…
The reduced dynamics formalism has recently emerged as a powerful tool to study the dynamics of non-equilibrium quantum impurity models in strongly correlated regimes. Examples include the non-equilibrium Anderson impurity model near the…
We present generalized adiabatic theorems for closed and open quantum systems that can be applied to slow modulations of rapidly varying fields, such as oscillatory fields that occur in optical experiments and light induced processes. The…
Polynomial dynamical systems are widely used to model and study real phenomena. In biochemistry, they are the preferred choice for modelling the concentration of chemical species in reaction networks with mass-action kinetics. These systems…
Controlling and understanding phenomena in coupled systems remains a significant challenge across diverse fields. This study investigates a simple globally coupled chemical system that exhibits a range of rich collective dynamics, from…
This work presents a comprehensive study of the generalized Duffing oscillator, a fundamental model in nonlinear dynamics described by the system $$ \dot{x} = y, \quad \dot{y} = -\alpha y - \epsilon x^m - \sigma x, $$ where $\epsilon \neq…
A theory determining the evolution of general Rayleigh-Taylor mixing fronts is established to reproduce firstly all of the documented experiments conducted for diverse acceleration histories and all density ratios. The theory is established…
We study generic holomorphic families of dynamical systems presenting problems of small divisors with fixed arithmetic. We prove that we have convergence for all parameter values or divergence everywhere except for an exceptional set in the…
The Riccati inequality and equality are studied for infinite dimensional linear discrete time stationary systems with respect to the scattering supply rate. The results obtained are an addition to and based on our earlier work on the…
Using an expansion in order parameters, the equation of motion for the centroid of globally coupled oscillators with natural frequencies taken from a distribution is obtained for the case of high coupling, low dispersion of natural…