Search results for "bifurcation"
showing 10 items of 204 documents
Quantum Criticality in a Bosonic Josephson Junction
2011
In this paper we consider a bosonic Josephson junction described by a two-mode Bose-Hubbard model, and we thoroughly analyze a quantum phase transition occurring in the system in the limit of infinite bosonic population. We discuss the relation between this quantum phase transition and the dynamical bifurcation occurring in the spectrum of the Discrete Self Trapping equations describing the system at the semiclassical level. In particular, we identify five regimes depending on the strength of the effective interaction among bosons, and study the finite-size effects arising from the finiteness of the bosonic population. We devote a special attention to the critical regime which reduces to th…
Paysages et choix d'itinéraires pédestres en milieu urbain. Une nouvelle approche par les bifurcations
2007
Walking has long been neglected in urban mobility research. In the context of a sustainable mobility, it is now included into numerous works including various approaches. The well-known models of flows affectation are often used to study the behaviour of pedestrians and to identify their preferences. However, the factors that are usually chosen to describe the urban environment are usually limited or inappropriate to the pedestrian movement. In addition, these models assume that the choices made by pedestrians are predetermined at the start of each trip, without any possible decision intervening along these trips. In this paper, we propose to test the role of urban landscape by using a new …
Families of Two-dimensional Vector Fields
1998
In this section we will consider individual vector fields. They can be considered as 0-parameter families. We assume these vector fields to be of class at least C 1. This will be sufficient to ensure the existence and uniqueness of the flow φ(t, x) (t is time, x ∈ S, the phase space) and the qualitative properties which we mention below.
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…
Positive and nodal solutions for nonlinear nonhomogeneous parametric neumann problems
2020
We consider a parametric Neumann problem driven by a nonlinear nonhomogeneous differential operator plus an indefinite potential term. The reaction term is superlinear but does not satisfy the Ambrosetti-Rabinowitz condition. First we prove a bifurcation-type result describing in a precise way the dependence of the set of positive solutions on the parameter λ > 0. We also show the existence of a smallest positive solution. Similar results hold for the negative solutions and in this case we have a biggest negative solution. Finally using the extremal constant sign solutions we produce a smooth nodal solution.
A proof of bistability for the dual futile cycle
2014
Abstract The multiple futile cycle is an important building block in networks of chemical reactions arising in molecular biology. A typical process which it describes is the addition of n phosphate groups to a protein. It can be modelled by a system of ordinary differential equations depending on parameters. The special case n = 2 is called the dual futile cycle. The main result of this paper is a proof that there are parameter values for which the system of ODE describing the dual futile cycle has two distinct stable stationary solutions. The proof is based on bifurcation theory and geometric singular perturbation theory. An important entity built of three coupled multiple futile cycles is…
Links and Bifurcations in Nonsingular Morse–Smale Systems
1997
Wada's theorem classifies the set of periodic orbits in NMS systems on S3 as links, that can be written in terms of six operations. This characterization allows us to study the topological restrictions that links require to suffer a given codimension one bifurcation. Moreover, these results are reproduced in the case of NMS systems with rotational symmetries, introducing new geometrical tools.
Socioemotional Wealth and Networking in the Internationalisation of Family SMEs
2021
In internationalisation processes, international expansion exposes family SMEs to external networking and the risks such expansion entails, and perceived threats to their socioemotional wealth (SEW) might restrain their willingness to take these actions. However, very few studies measure SEW and associate it with internationalisation. Considering SEW preservation’s prominence in family SMEs and SMEs’ heavy dependence on networking during internationalisation, we hypothesise that SEW preservation has a negative association and networking has a positive association with the family SMEs’ degree of internationalisation (DOI). We reconstruct four SEW constructs that carry significance for family…