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Related papers: Control of Dynamic Hopf Bifurcations

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For piecewise-smooth ordinary differential equations, the occurrence of a Hopf bifurcation on a switching surface is known as a boundary Hopf bifurcation. Boundary Hopf bifurcations are codimension-two, so occur at points in two-parameter…

Dynamical Systems · Mathematics 2026-04-09 David J. W. Simpson

In this paper, we analyze some local stability and local bifurcation properties of the Proportionally fair, TCP fair, and the Delay-based dual algorithms in the presence of two distinct time delays. In particular, our focus is on the…

Chaotic Dynamics · Physics 2019-06-19 Abuthahir Abuthahir , Gaurav Raina

We propose a paradigmatic model system, a subcritical Hopf normal form subjected to noise and time-delayed feedback, to investigate the impact of time delay on coherence resonance in non-excitable systems. We develop analytical tools to…

Adaptation and Self-Organizing Systems · Physics 2014-12-08 Paul M. Geffert , Anna Zakharova , Andrea Vüllings , Wolfram Just , Eckehard Schöll

A general FitzHugh-Rinzel model, able to describe several neuronal phenomena, is considered. Linear stability and Hopf bifurcations are investigated by means of the spectral equation for the ternary autonomous dynamical system and the…

Chaotic Dynamics · Physics 2025-03-04 Monica De Angelis

We study the weakly nonlinear saturation of the flutter instability of a planar Cosserat rod in a viscous fluid driven by a terminal follower force. This instability, established in our preceding work as a Hopf bifurcation of a…

Mathematical Physics · Physics 2026-05-15 Mohamed Warda

We study elastic snap-through induced by a control parameter that evolves dynamically. In particular, we study an elastic arch subject to an end-shortening that evolves linearly with time, i.e. at a constant rate. For large end-shortening…

Soft Condensed Matter · Physics 2025-11-07 Mingchao Liu , Michael Gomez , Dominic Vella

Circular domains frequently appear in the fields of ecology, biology and chemistry. In this paper, we investigate the equivariant Hopf bifurcation of partial functional differential equations with Neumann boundary condition on a…

Dynamical Systems · Mathematics 2023-05-11 Yaqi Chen , Xianyi Zeng , Ben Niu

Many physical systems exhibit limit cycle oscillations induced by Hopf bifurcations. In aerospace engineering, limit cycle oscillations arise from undesirable Hopf bifurcation phenomena such as aeroelastic flutter and transonic buffet. In…

Dynamical Systems · Mathematics 2025-11-07 Sicheng He , Max Howell , Daning Huang , Eirikur Jonsson , Galen W. Ng , Joaquim R. R. A. Martins

It is well-established that shear flows are linearly unstable provided the viscosity is small enough, when the horizontal Fourier wave number lies in some interval, between the so-called lower and upper marginally stable curves. In this…

Analysis of PDEs · Mathematics 2025-10-09 Dongfen Bian , Emmanuel Grenier , Gérard Iooss

Our concern is the study of degenerate Hopf bifurcation of smooth planar dynamical systems near isolated singular points. To do so, we propose to split up the definition of degeneracy into two types. Degeneracy of first kind shall means…

Dynamical Systems · Mathematics 2009-12-17 Mariano Rodriguez Ricard

An algorithm is presented here, for discovering Hopf-Bifurcation varieties of polynomial dynamical systems. It is based on the expression of specific polynomials, as sums of products of first degree polynomials, with parametrical…

Chaotic Dynamics · Physics 2008-07-29 Stelios Kotsios

It is known that Lotka - Volterra type differential equations with delays or distributed delays have an important role in modeling ecological systems. In this paper we study the effects of distributed delay on the dynamics of the harvested…

Dynamical Systems · Mathematics 2013-11-12 Chol Kim

The memory-based diffusion systems have wide applications in practice. Hopf bifurcations are observed from such systems. To meet the demand for computing the normal forms of the Hopf bifurcations of such systems, we develop an effective new…

Dynamical Systems · Mathematics 2021-04-02 Yongli Song , Yahong Peng , Tonghua Zhang

This paper is devoted to the study of the stability of limit cycles of a nonlinear delay differential equation with a distributed delay. The equation arises from a model of population dynamics describing the evolution of a pluripotent stem…

Analysis of PDEs · Mathematics 2009-04-17 Mostafa Adimy , Fabien Crauste , Andrei Halanay , Mihaela Neamtu , Dumitru Opris

A singular perturbation problem from the artificial compressible system to the incompressible system is considered for a doubly diffusive convection when a Hopf bifurcation from the motionless state occurs in the incompressible system. It…

Analysis of PDEs · Mathematics 2021-05-26 Chun-Hsiung Hsia , Yoshiyuki Kagei , Takaaki Nishida , Yuka Teramoto

This paper shows that the variance of load bus voltage magnitude in a small power system test case increases monotonically as the system approaches a Hopf bifurcation. This property can potentially be used as a method for monitoring…

Chaotic Dynamics · Physics 2016-11-18 Goodarz Ghanavati , Paul D. H. Hines , Taras I. Lakoba

Complex dynamical systems may exhibit multiple steady states, including time-periodic limit cycles, where the final trajectory depends on initial conditions. With tuning of parameters, limit cycles can proliferate or merge at an exceptional…

Statistical Mechanics · Physics 2024-12-03 Sergei Shmakov , Peter B. Littlewood

If one wants to explore the properties of a dynamical system systematically one has to be able to track equilibria and periodic orbits regardless of their stability. If the dynamical system is a controllable experiment then one approach is…

Dynamical Systems · Mathematics 2009-03-19 Jan Sieber , Bernd Krauskopf

In this article, the phenomenon of delayed Hopf bifurcations (DHB) in reaction-diffusion PDEs is analyzed in the cubic Complex Ginzburg-Landau equation with a slowly-varying parameter. We use the classical asymptotic methods of stationary…

Dynamical Systems · Mathematics 2020-12-21 Ryan Goh , Tasso J. Kaper , Theodore Vo

The loss of stability of induction motor controlled by Indirect Field Oriented Control (IFOC) is a matter of great concern of operators and design engineers. This paper reports indices to detect and predict stability problem such as system…

Chaotic Dynamics · Physics 2014-10-28 Krishnendu Chakrabarty , Urmila Kar