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Sudden singularities occur in FRW spacetimes when the scale factor remains finite and different from zero while some of its derivatives diverge. After proper rescaling, the scale factor close to such a singularity at $t=0$ takes the form…

General Relativity and Quantum Cosmology · Physics 2016-12-21 Leandros Perivolaropoulos

We show that a simple piecewise-linear system with time delay and periodic forcing gives rise to a rich bifurcation structure of torus bifurcations and Arnold tongues, as well as multistability across a significant portion of the parameter…

Chaotic Dynamics · Physics 2020-02-11 Pierce Ryan , Andrew Keane , Andreas Amann

For three-dimensional piecewise-smooth systems of ordinary differential equations, this paper characterises the stability of points that belong to a switching surface and are equilibria of exactly one of the two neighbouring pieces of the…

Dynamical Systems · Mathematics 2026-02-10 David J. W. Simpson

This study investigates the low-frequency dynamics of a turbulent separation bubble (TSB) over a backward-facing ramp, with a focus on large-scale coherent structures associated with the so-called 'breathing motion'. Using time-resolved…

We consider phase transitions, in the form of spontaneous symmetry breaking (SSB) bifurcations of solitons, in dual-core couplers with fractional diffraction and cubic self-focusing acting in each core, characterized by Levy index $\alpha$.…

Pattern Formation and Solitons · Physics 2023-06-21 Dmitry V. Strunin , Boris A. Malomed

To explain the phenomenon of bifurcation delay, which occurs in planar systems of the form $\dot{x}=\epsilon f(x,z,\epsilon)$, $\dot{z}=g(x,z,\epsilon)z$, where $f(x,0,0)>0$ and $g(x,0,0)$ changes sign at least once on the $x$-axis, we use…

Dynamical Systems · Mathematics 2016-11-09 Ting-Hao Hsu

We furnish necessary and sufficient conditions for the occurrence of a Hopf bifurcation in a particularly significant fluid-structure problem, where a Navier-Stokes liquid interacts with a rigid body that is subject to an undamped elastic…

Analysis of PDEs · Mathematics 2024-06-07 Denis Bonheure , Giovanni P. Galdi , Filippo Gazzola

The bifurcation structure of coupled periodically driven double-well Duffing oscillators is investigated as a function of the strength of the driving force $f$ and its frequency $\Omega$. We first examine the stability of the steady state…

Chaotic Dynamics · Physics 2015-06-26 Anatole Kenfack

We show that $J-$ stability is open and dense in natural families of meromorphic maps of one complex variable with a finite number of singular values, and even more generally, to finite type maps. This extends the results of…

Dynamical Systems · Mathematics 2023-09-20 Matthieu Astorg , Anna Miriam Benini , Núria Fagella

We study bifurcation behavior in periodic perturbations of two-dimensional symmetric systems exhibiting codimension-two bifurcations with a double eigenvalue when the frequencies of the perturbation terms are small. We transform the…

Dynamical Systems · Mathematics 2023-02-15 Kazuyuki Yagasaki

Quantifying the stability of an equilibrium is central in the theory of dynamical systems as well as in engineering and control. A comprehensive picture must include the response to both small and large perturbations, leading to the…

Adaptation and Self-Organizing Systems · Physics 2023-03-08 Philipp C. Böttcher , Benjamin Schäfer , Stefan Kettemann , Carsten Agert , Dirk Witthaut

We perform both analytical and numerical bifurcation analysis of a forest-grassland ecosystem model coupled with human interaction. The model consists of two nonlinear ordinary differential equations incorporating the human perception of…

Numerical Analysis · Mathematics 2023-03-16 Konstantinos Spiliotis , Lucia Russo , Francesco Giannino , Constantinos Siettos

We revisit the classic stability problem of the buckling of an inextensible, axially compressed beam on a nonlinear elastic foundation with a semi-analytical approach to understand how spatially localized deformation solutions emerge in…

Pattern Formation and Solitons · Physics 2020-09-03 Shrinidhi S. Pandurangi , Ryan S. Elliott , Timothy J. Healey , Nicolas Triantafyllidis

We investigate the slow passage through a pitchfork bifurcation in a spatially extended system, when the onset of instability is slowly varying in space. We focus here on the critical parameter scaling, when the instability locus propagates…

Dynamical Systems · Mathematics 2024-01-12 Ryan Goh , Tasso J. Kaper , Arnd Scheel

Boundary effects are crucial for dynamics of dilute charged gases governed by the Vlasov-Poisson-Boltzmann (VPB) system. In this paper, we study the existence and regularity of solutions to the VPB system with soft potential in a bounded…

Analysis of PDEs · Mathematics 2021-11-18 Fucai Li , Yichun Wang

We consider the SIRWJS epidemiological model that includes the waning and boosting of immunity via secondary infections. We carry out combined analytical and numerical investigations of the dynamics. The formulae describing the existence…

Populations and Evolution · Quantitative Biology 2023-05-16 Richmond Opoku-Sarkodie , Ferenc A. Bartha , Mónika Polner , Gergely Röst

Saffman and Turner (1957) argued that the collision rate for droplets in turbulence increases as the turbulent strain rate increases. But the numerical simulations of Dhanasekaran et al. (2021) in a steady straining flow show that the…

Fluid Dynamics · Physics 2022-06-22 A. Dubey , K. Gustavsson , G. Bewley , B. Mehlig

The tippedisk is a mathematical-mechanical archetype for a peculiar friction-induced instability phenomenon leading to the inversion of an unbalanced spinning disk, being reminiscent to (but different from) the well-known inversion of the…

Classical Physics · Physics 2021-12-09 Simon Sailer , Remco I. Leine

Inspired by an example of Grebogi et al [1], we study a class of model systems which exhibit the full two-step scenario for the nonautonomous Hopf bifurcation, as proposed by Arnold [2]. The specific structure of these models allows a…

Dynamical Systems · Mathematics 2013-05-08 Vasso Anagnostopoulou , Tobias Jäger , Gerhard Keller

In this paper we consider the one dimensional spring-block model describing earthquake faulting. By using geometric singular perturbation theory and the blow-up method we provide a detailed description of the periodicity of the earthquake…

Dynamical Systems · Mathematics 2017-06-28 Elena Bossolini , Morten Brøns , Kristian Uldall Kristiansen