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The present paper addresses the swing equation with additional delayed damping as an example for pendulum-like systems. In this context, it is proved that recurring sub- and supercritical Hopf bifurcations occur if time delay is increased.…

Dynamical Systems · Mathematics 2019-12-23 Tessina H. Scholl , Lutz Gröll , Veit Hagenmeyer

We derive a Cram\'er-Rao lower bound for the variance of Floquet multiplier estimates that have been constructed from stable limit cycles perturbed by noise. To do so, we consider perturbed periodic orbits in the plane. We use a periodic…

Dynamical Systems · Mathematics 2017-11-30 Aurya Javeed

Dynamics in delayed differential equations (DDEs) is a well studied problem mainly because DDEs arise in models in many areas of science including biology, physiology, population dynamics and engineering. The change of the nature in the…

We present a result concerning the mean value of orbits emerging from Hopf bifurcations. We then apply this result to identify a new phenomenon termed {\it oscillation-induced gain modulation}. A Hopf bifurcation of a system $\dot{x} = f(x;…

Dynamical Systems · Mathematics 2025-10-07 William Harold Nesse , Cooper John Hutchinson

We study the emergence of symmetric oscillatory behavior in multi-agent systems where each agent incorporates a continuous memory of its past states and past rates of change, modeled by distributed retarded and neutral delays. The…

Dynamical Systems · Mathematics 2026-04-23 Casey Crane

Double Hopf bifurcation analysis can be used to reveal some complicated dynamical behavior in a dynamical system, such as the existence or coexistence of periodic orbits, quasi-periodic orbits, or even chaos. In this paper, an algorithm for…

Dynamical Systems · Mathematics 2018-11-27 Yanfei Du , Ben Niu , Yuxiao Guo , Junjie Wei

We analyze the nonlinear dynamics near the incoherent state in a mean-field model of coupled oscillators. The population is described by a Fokker-Planck equation for the distribution of phases, and we apply center-manifold reduction to…

patt-sol · Physics 2009-10-22 John David Crawford

A Hopf bifurcation theorem is established for the abstract evolution equation $\frac{\mathrm{d}x}{\mathrm{d}t}=F(x,\lambda)$ in infinite dimensions under the degeneracy condition $Re \mu ^{\prime}(\lambda_0)= 0$ and suitable assumptions.…

Functional Analysis · Mathematics 2022-04-26 Hongjing Pan , Ruixiang Xing , Zhannan Zhuang

We explain the setup for using the pde2path libraries for Hopf bifurcation and continuation of branches of periodic orbits and give implementation details of the associated demo directories. See [Uecker, Comm. in Comp. Phys., 2019] for a…

Numerical Analysis · Mathematics 2020-04-28 Hannes Uecker

We present a delayed feedback control (DFC) mechanism for stabilizing cycles of one dimensional discrete time systems. In particular, we consider a delayed feedback control for stabilizing $T$-cycles of a differentiable function $f:…

Optimization and Control · Mathematics 2015-01-20 D. Dmitrishin , P. Hagelstein , A. Khamitova , A. Stokolos

We present a linear model, which mimics the response of a spatially extended dissipative medium to a distant perturbation, and investigate its dynamics under delayed feedback control. The time a perturbation needs to propagate to a…

Adaptation and Self-Organizing Systems · Physics 2018-11-08 Josua Grawitter , Reinier van Buel , Christian Schaaf , Holger Stark

We present a microscopic theory of fluctuation-mediated pairing mechanism in a two-dimensional extended Hubbard model. In contrast to conventional wisdom, odd-frequency spin-triplet pairing can be stabilized near the spin-density-wave…

Superconductivity · Physics 2008-06-27 Keiji Yada , Seiichiro Onari , Yukio Tanaka , Kazumasa Miyake

Dynamics in delayed differential equations (DDEs) is a well studied problem mainly because DDEs arise in models in many areas of science including biology, physiology, population dynamics and engineering. The change of nature in the…

The present paper investigates the structural stability of bidirectional cyclic negative feedback systems. To address this, we develop a generalized Floquet theory and construct nested invariant cones for the systems. Subsequently, we…

Dynamical Systems · Mathematics 2025-10-10 Xu Cheng , Yi Wang , Dun Zhou

An experimental study of bifurcations associated with stability of stationary points (SP's) in a parametrically forced magnetic pendulum and a comparison of its results with numerical results are presented. The critical values for which the…

chao-dyn · Physics 2008-02-03 Sang-Yoon Kim , S. H. Shin , J. Yi , J. W. Jang

This paper pursues the study carried out by the authors in {\it Stability and Hopf bifurcation in the Watt governor system} \cite{smb}, focusing on the codimension one Hopf bifurcations in the centrifugal Watt governor differential system,…

Dynamical Systems · Mathematics 2007-05-23 Jorge Sotomayor , Luis Fernando Mello , Denis de Carvalho Braga

For many physical systems the transition from a stationary solution to sustained small amplitude oscillations corresponds to a Hopf bifurcation. For systems involving impacts, thresholds, switches, or other abrupt events, however, this…

Dynamical Systems · Mathematics 2019-05-07 David J. W. Simpson

We examine a strange chaotic attractor and its unstable periodic orbits in case of one degree of freedom nonlinear oscillator with non symmetric potential. We propose an efficient method of chaos control stabilizing these orbits by a…

Chaotic Dynamics · Physics 2015-06-26 G. Litak , M. Ali , L. M. Saha

We prove a necessary and sufficient criterion for the exponential stability of periodic solutions of delay differential equations with large delay. We show that for sufficiently large delay the Floquet spectrum near criticality is…

Dynamical Systems · Mathematics 2015-03-17 Jan Sieber , Matthias Wolfrum , Mark Lichtner , Serhiy Yanchuk

A ferrofluid droplet confined in a Hele-Shaw cell can be deformed into a stably spinning ``gear,'' using crossed magnetic fields. Previously, fully nonlinear simulation revealed that the spinning gear emerges as a stable traveling wave…

Pattern Formation and Solitons · Physics 2023-05-19 Zongxin Yu , Ivan C. Christov