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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…
This study investigates the existence and stability of limit cycles resulting from self-excited oscillations in linear multi-degree-of-freedom systems subjected to discontinuous, state-dependent forcing. Using the method of averaging and…
A novel adaptive control approach is proposed to solve the globally asymptotic state stabilization problem for uncertain pure-feedback nonlinear systems which can be transformed into the pseudo-affine form. The pseudo-affine pure-feedback…
We consider a model proposed by one of the authors for a type of plastic instability found in creep experiments which reproduces a number of experimentally observed features. The model consists of three coupled non-linear differential…
This paper investigates model-order reduction methods for geometrically nonlinear structures. The parametrisation method of invariant manifolds is used and adapted to the case of mechanical systems expressed in the physical basis, so that…
The Multi-Phase Transport model (AMPT) is used to study the effects of the parton-scattering cross-sections ($\sigma_{pp}$) and hadronic re-scattering on the linear contributions to the flow harmonic $\textit{v}_{4}$, the non-linear…
This work is a theoretical investigation of the stability of the non-linear behavior of an oscillating tip-cantilever system used in dynamic force microscopy. Stability criterions are derived that may help to a better understanding of the…
Nonlinear contraction theory is a comparatively recent dynamic control system design tool based on an exact differential analysis of convergence, in essence converting a nonlinear stability problem into a linear time-varying stability…
Flutter stability is a dominant design constraint of modern gas and steam turbines. To further increase the feasible design space, flutter-tolerant designs are currently explored, which may undergo Limit Cycle Oscillations (LCOs) of…
In Hamiltonian systems subjected to periodic perturbations the stable and unstable manifolds of the unstable periodic orbits provide the dynamical "skeleton" that drives the mixing process and bounds the chaotic regions of the phase space.…
Researchers have developed hybrid Van der Pol Rayleigh Duffing type oscillators to model human induced forces; however, their analytical framework has largely relied on the Lindstedt Poincare perturbation method, energy balance approaches,…
Although stable solutions of dynamical systems are typically considered more important than unstable ones, unstable solutions have a critical role in the dynamical integrity of stable solutions. In fact, usually, basins of attraction…
The instability in the selection of models is a major concern with data sets containing a large number of covariates. We focus on stability selection which is used as a technique to improve variable selection performance for a range of…
A sharp stability analysis of atomistic-to-continuum coupling methods is essential for evaluating their capabilities for predicting the formation and motion of lattice defects. We formulate a simple one-dimensional model problem and give a…
We study a three-dimensional dynamical system in two slow variables and one fast variable. We analyze the tangency of the unstable manifold of an equilibrium point with "the" repelling slow manifold, in the presence of a stable periodic…
The stability analysis of elastic rings subjected to various loading conditions is examined, focusing on stable and unstable configurations. The harmonic balance method is employed to investigate the stability range under different loading…
Real applications in structural mechanics, where the dynamic behavior is linear, are rare. Usually, structures are made of components assembled together by means of joints whose behavior maybe highly nonlinear. Depending on the amount of…
This paper presents a general framework to derive the weakly nonlinear stability near a Hopf bifurcation in a special class of multi-scale reaction-diffusion equations. The main focus is on how the linearity and nonlinearity of the fast…
Many physical systems can be modelled as parameter-dependent variational problems. In numerous cases, multiple equilibria co-exist, requiring the evaluation of their stability, and the monitoring of transitions between them. Generally, the…
Amplitude expansions are used to determine steady states of a semi-infinite solid subject to the Grinfeld instability in systems with a fixed (wave)length. We present two methods to obtain high-order weakly nonlinear results. Using the…