相关论文: Destabilization of synchronous periodic solutions …
Acoustic waves in a slightly compressible fluid saturating porous periodic structure are studied using two complementary approaches: 1) the periodic homogenization (PH) method provides effective model equations for a general dynamic problem…
The phase reduction method for limit cycle oscillators subjected to weak perturbations has significantly contributed to theoretical investigations of rhythmic phenomena. We here propose a generalized phase reduction method that is also…
We consider the symmetry-breaking steady state bifurcation of a spatially-uniform equilibrium solution of E(2)-equivariant PDEs. We restrict the space of solutions to those that are doubly-periodic with respect to a square or hexagonal…
In several studies it has been observed that, when using stabilised $\mathbb{P}_k^{}\times\mathbb{P}_k^{}$ elements for both velocity and pressure, the error for the pressure is smaller, or even of a higher order in some cases, than the one…
The aim of this paper is to provide an effective framework for analysing bifurcations of equilibria in nonlinearly periodically forced delay differential equations. First, we establish the existence of a periodic smooth finite-dimensional…
The phenomenology of a system of two coupled quadratic maps is studied both analytically and numerically. Conditions for synchronization are given and the bifurcations of periodic orbits from this regime are identified. In addition, we show…
In this paper, a mathematical model of pneumococcal pneumonia with time delays is proposed. The stability theory of delay differential equations is used to analyze the model. The results show that the disease-free equilibrium is…
We provide an experimental framework where periodically driven PT-symmetric systems can be investigated. The set-up, consisting of two UHF oscillators coupled by a time-dependent capacitance, demonstrates a cascade of PT-symmetric broken…
The transport of charged particles or photons in a scattering medium can be modelled with a Boltzmann equation. The mathematical treatment for scattering in such scenarios is often simplified if evaluated in a frame where the scattering…
In this paper, we consider a general single population model with delay and patch structure, which could model the population loss during the dispersal. It is shown that the model admits a unique positive equilibrium when the dispersal rate…
In this paper we present a general approach to rigorously validate Hopf bifurcations as well as saddle-node bifurcations of periodic orbits in systems of ODEs. By a combination of analytic estimates and computer-assisted calculations, we…
Existence and stability of time periodic solutions for nonlinear elastic wave equations with viscoelastic terms are established. The existence of the time periodic solution is proved using the spectral decomposition of the linear principal…
A four-dimensional mathematical model of the hypothalamus-pituitary-adrenal (HPA) axis is investigated, incorporating the influence of the GR concentration and general feedback functions. The inclusion of distributed time delays provides a…
The design of robust orbitally stabilizing feedback is considered. From a known orbitally stabilizing controller for a nominal, disturbance-free system, a robustifying feedback extension is designed utilizing the sliding-mode control (SMC)…
We present analytical and numerical results on the joint dynamics of two coupled Duffing oscillators with nonlinearity of opposite signs (hardening and softening). In particular, we focus on the existence and stability of synchronized…
A mathematical model describing the initial stage of the capture of oscillatory systems into autoresonance under the action of slowly varying pumping is considered. Solutions with an infinitely growing amplitude are associated with the…
Wave propagation and acoustic scattering problems require vast computational resources to be solved accurately at high frequencies. Asymptotic methods can make this cost potentially frequency independent by explicitly extracting the…
A rigorous Floquet mode analysis is proposed for a zero thickness space-time modulated Huygens' metasurface to model and determine the strengths of the new harmonic components of the scattered fields. The proposed method is based on…
Our aim in this paper is twofold. Firstly, we develop a new asymptotic theory for Floquet exponents. We consider a linear system of differential equations with a time-periodic coefficient matrix. Assuming that the coefficient matrix depends…
An optoelectronic oscillator exhibiting a large delay in its feedback loop is studied both experimentally and theoretically. We show that multiple square-wave oscillations may coexist for the same values of the parameters…