Search results for " Bifurcation"

Mixed-mode oscillation-incrementing bifurcations and a devil’s staircase from a nonautonomous, constrained Bonhoeffer-van der Pol oscillator

2018

Asymmetric balance in symmetry breaking

2020

Spontaneous symmetry breaking is central to our understanding of physics and explains many natural phenomena, from cosmic scales to subatomic particles. Its use for applications requires devices with a high level of symmetry, but engineered systems are always imperfect. Surprisingly, the impact of such imperfections has barely been studied, and restricted to a single asymmetry. Here, we experimentally study spontaneous symmetry breaking with two controllable asymmetries. We remarkably find that features typical of spontaneous symmetry breaking, while destroyed by one asymmetry, can be restored by introducing a second asymmetry. In essence, asymmetries are found to balance each other. Our st…

Bifurcation and multiplicity results for nonlinear elliptic problems involving critical Sobolev exponents

1984

Abstract In this paper we study the existence of nontrivial solutions for the boundary value problem { − Δ u − λ u − u | u | 2 ⁎ − 2 = 0 in Ω u = 0 on ∂ Ω when Ω⊂Rn is a bounded domain, n ⩾ 3, 2 ⁎ = 2 n ( n − 2 ) is the critical exponent for the Sobolev embedding H 0 1 ( Ω ) ⊂ L p ( Ω ) , λ is a real parameter. We prove that there is bifurcation from any eigenvalue λj of − Δ and we give an estimate of the left neighbourhoods ] λ j ⁎ , λj] of λj, j∈N, in which the bifurcation branch can be extended. Moreover we prove that, if λ ∈ ] λ j ⁎ , λj[, the number of nontrivial solutions is at least twice the multiplicity of λj. The same kind of results holds also when Ω is a compact Riemannian manif…

Control of a Non-isothermal CSTR by Type-2 Fuzzy Logic Controllers

2009

The paper describes the application of a type-2 fuzzy logic controller (FLC) to a non-isothermal continuous stirred tank reactor (CSTR) characterized by the presence of saddle node and Hopf bifurcations. Its performance is compared with a type-1 fuzzy logic controller performance. A full analysis of the uncontrolled CSTR dynamic was carried out and used for the feedback-feedforward fuzzy controllers development. Simulation results confirm the effectiveness and the robustness of the type-2 FLCs which outperform their type-1 counterparts, particularly when uncertainties are present in the system.

Control of a nonlinear continuous bioreactor with bifurcation by a type-2 fuzzy logic controller

2008

The object of this paper is the application of a type-2 fuzzy logic controller to a nonlinear system that presents bifurcations. A bifurcation can cause instability in the system or can create new working conditions which, although stable, are unacceptable. The only practical solution for an efficient control is the use of high performance controllers that take into account the uncertainties of the process. A type-2 fuzzy logic controller is tested by simulation on a nonlinear bioreactor system that is characterized by a transcritical bifurcation. Simulation results show the validity of the proposed controllers in preventing the system from reaching bifurcation and instable or undesirable s…

Control of a non-isothermal continuous stirred tank reactor by a feedback–feedforward structure using type-2 fuzzy logic controllers

2011

A control system that uses type-2 fuzzy logic controllers (FLC) is proposed for the control of a non-isothermal continuous stirred tank reactor (CSTR), where a first order irreversible reaction occurs and that is characterized by the presence of bifurcations. Bifurcations due to parameter variations can bring the reactor to instability or create new working conditions which although stable are unacceptable. An extensive analysis of the uncontrolled CSTR dynamics was carried out and used for the choice of the control configuration and the development of controllers. In addition to a feedback controller, the introduction of a feedforward control loop was required to maintain effective control…

Pattern formation driven by cross-diffusion

2009

In this work we are interested in describing the mechanism of pattern formation for a reaction-diffusion system with nonlinear diffusion terms (which take into account the self and the cross-diffusion effects). The reaction terms are chosen of the Lotka-Volterra type in the competitive interaction case. The cross-diffusion is proved to be the key mechanism of pattern formation via a linear stability analysis. A weakly nonlinear multiple scales analysis is carried out to predict the amplitude and the form of the pattern close to the bifurcation threshold. In particular, the Stuart-Landau equation which rules the evolution of the amplitude of the most unstable mode is found. In the subcritica…

Real-Life Outcomes of Coronary Bifurcation Stenting in Acute Myocardial Infarction (Zabrze–Opole Registry)

2021

Percutaneous coronary intervention (PCI) of bifurcation lesions is a technical challenge associated with high risk of adverse events, especially in primary PCI. The aim of the study is to analyze long-term outcomes after PCI for coronary bifurcation in acute myocardial infarction (AMI). The outcome was defined as the rate of major adverse cardiac event related to target lesion failure (MACE-TLF) (death-TLF, nonfatal myocardial infarction-TLF and target lesion revascularization (TLR)) and the rate of stent thrombosis (ST). From 306 patients enrolled to the registry, 113 were diagnosed with AMI. In the long term, AMI was not a risk factor for MACE-TLF. The risk of MACE-TLF was dependent on th…

On Bifurcation Analysis of Implicitly Given Functionals in the Theory of Elastic Stability

2015

In this paper, we analyze the stability and bifurcation of elastic systems using a general scheme developed for problems with implicitly given functionals. An asymptotic property for the behaviour of the natural frequency curves in the small vicinity of each bifurcation point is obtained for the considered class of systems. Two examples are given. First is the stability analysis of an axially moving elastic panel, with no external applied tension, performing transverse vibrations. The second is the free vibration problem of a stationary compressed panel. The approach is applicable to a class of problems in mechanics, for example in elasticity, aeroelasticity and axially moving materials (su…

Weakly nonlinear analysis of Turing patterns in a morphochemical model for metal growth

2015

We focus on the morphochemical reaction–diffusion model introduced in Bozzini et al. (2013) and carry out a nonlinear bifurcation analysis with the aim to characterize the shape and the amplitude of the patterns arising as the result of Turing instability of the physically relevant equilibrium. We perform a weakly nonlinear multiple scales analysis, and derive the normal form equations governing the amplitude of the patterns. These amplitude equations allow us to construct relevant solutions of the model equations and reveal the presence of multiple branches of stable solutions arising as the result of subcritical bifurcations. Hysteretic type phenomena are highlighted also through numerica…