Search results for "bifurcation"
showing 10 items of 204 documents
Behavior of gap solitons in anharmonic lattices
2017
International audience; Using the theory of bifurcation, we provide and find gap soliton dynamics in a nonlinear Klein-Gordon model with anharmonic, cubic, and quartic interactions immersed in a parametrized on-site substrate potential. The case of a deformable substrate potential allows theoretical adaptation of the model to various physical situations. Nonconvex interactions in lattice systems lead to a number of interesting phenomena that cannot be produced with linear coupling alone. By investigating the dynamical behavior and bifurcations of solutions of the planar dynamical systems, we derive a variety of exotic solutions corresponding to the phase trajectories under different paramet…
Asset price dynamics in a “bull and bear market”
2021
Abstract We generalize an existing asset market model with heterogenous agents. In particular, we consider the case in which no-trade and low-trade intervals of chartists and fundamentalists respectively are not congruent. Thus we model chartist and fundamentalists who respond to asset prices in agent-specific neighborhoods around the fundamental value with different trade intensities. The resulting asset price dynamics is generated by a one-dimensional 5-piece linear map with discontinuities. Our analysis of this map focusses on coexisting price equilibria. Conditions for their existence and stability are determined analytically. By visualizing the results we allow for a basic bifurcation …
Four-wave mixing and vacuum squeezing in polariton microcavities
2017
In a recent paper [1] it has been shown how a bichromatic fast driving of optomechanical (optical domain) and superconducting circuit systems (microwave domain), operating in a limit where they present a non-linear Kerr-type interaction, can give rise to very strong vacuum squeezing. The driving with two close frequencies of a Kerr cavity changes the usual bistability bifurcation behaviour that takes place under monochromatic driving, into a degenerate four-wave mixing bifurcation, where a phase-bistable component starts oscillating spontaneously at a frequency that lies halfway between the two driving frequencies [2]. This resembles the physics of the optical parametric oscillator threshol…
Observation of Poincaré-Andronov-Hopf Bifurcation in Cyclotron Maser Emission from a Magnetic Plasma Trap
2018
We report the first experimental evidence of a controlled transition from the generation of periodic bursts of electromagnetic radiation into the continuous-wave regime of a cyclotron maser formed in magnetically confined nonequilibrium plasma. The kinetic cyclotron instability of the extraordinary wave of weakly inhomogeneous magnetized plasma is driven by the anisotropic electron population resulting from electron cyclotron plasma heating in a MHD-stable minimum-B open magnetic trap. peerReviewed
Optimization model predictions for postural coordination modes
2003
International audience; This paper examines the ability of the dynamic optimization model to predict changes between in-phase and anti-phase postural modes of coordination and to evaluate influence of two particular environmental and intentional constraints on postural strategy. The task studied was based on an experimental paradigm that consisted in tracking a target motion with the head. An original optimal procedure was developed for cyclic problems to calculate hip and ankle angular trajectories during postural sway with a minimum torque change criterion. Optimization results give a good description of the sudden bifurcation phase between in-phase and anti-phase postural coordination mo…
Control of the Biodegradation of Mixed Wastes in a Continuous Bioreactor by a Type-2 Fuzzy Logic Controller
2009
Abstract Type-2 fuzzy logic control is proposed for nonlinear processes characterized by bifurcations. A control simulation study was conducted for a bioreactor with cell recycle containing phenol and glucose as carbon and energy sources in which a pure culture of Pseudomonas putida is carried out. The model developed by Ajbar [Ajbar, A. (2001). Stability analysis of the biodegradation of mixed wastes in a continuous bioreactor with cell recycle. Water Research, 35 (5), 1201–1208] was used for the simulations. The particular dynamics of the bioreactor, characterized by two saddle-node bifurcations, makes its control difficult, since it may become unstable also for small variations of some p…
On basins of attraction for a predator-prey model via meshless approximation
2016
Abstract. In this work an epidemiological predator-prey model is studied. It analyzes the spread of an infectious disease with frequency-dependent and vertical transmission within the predator population. In particular we consider social predators, i.e. they cooperate in groups to hunt. The result is a three-dimensional system in which the predator population is divided into susceptible and infected individuals. Studying the dynamical system and bifurcation diagrams, a scenario was identified in which the model shows multistability but the domain of attraction of one equilibrium point can be so small that it is almost the point itself. From a biological point of view it is important to anal…
Bifurcation analysis of a TaO memristor model
2019
This paper presents a study of bifurcation in the time-averaged dynamics of TaO memristors driven by narrow pulses of alternating polarities. The analysis, based on a physics-inspired model, focuses on the stable fixed points and on how these are affected by the pulse parameters. Our main finding is the identification of a driving regime when two stable fixed points exist simultaneously. To the best of our knowledge, such bistability is identified in a single memristor for the first time. This result can be readily tested experimentally, and is expected to be useful in future memristor circuit designs.
Route to chaos in the weakly stratified Kolmogorov flow
2019
We consider a two-dimensional fluid exposed to Kolmogorov’s forcing cos(ny) and heated from above. The stabilizing effects of temperature are taken into account using the Boussinesq approximation. The fluid with no temperature stratification has been widely studied and, although relying on strong simplifications, it is considered an important tool for the theoretical and experimental study of transition to turbulence. In this paper, we are interested in the set of transitions leading the temperature stratified fluid from the laminar solution [U∝cos(ny),0, T ∝ y] to more complex states until the onset of chaotic states. We will consider Reynolds numbers 0 < Re ≤ 30, while the Richardson numb…
Chaotic behavior in deformable models: the double-well doubly periodic oscillators
2001
Abstract The motion of a particle in a one-dimensional perturbed double-well doubly periodic potential is investigated analytically and numerically. A simple physical model for calculating analytically the Melnikov function is proposed. The onset of chaos is studied through an analysis of the phase space, a construction of the bifurcation diagram and a computation of the Lyapunov exponent. The parameter regions of chaotic behavior predicted by the theoretical analysis agree very well with numerical simulations.