Non-quantum chirality in a driven Brusselator

2022 ◽  
Author(s):  
Jason Gallas
Keyword(s):  
High Resolution ◽  
Phase Diagrams ◽  
Equations Of Motion ◽  
Rate Equations ◽  
Periodic Oscillations ◽  
Local Maxima ◽  
Periodically Driven ◽  
Stable Periodic

Abstract We report the discovery of non-quantum chirality in the a periodically driven Brusselator. In contrast to standard chirality from quantum contexts, this novel type of chirality is governed by rate equations, namely by purely classical equations of motion. The Brusselator chirality was found by computing high-resolution phase diagrams depicting the number of spikes, local maxima, observed in stable periodic oscillations of the Brusselator as a function of the frequency and amplitude of the external drive. We also discuss how to experimentally observed non-quantum chirality in generic oscillators governed by nonlinear sets of rate equations.

Periodic oscillations of the forced Brusselator

2015 ◽  
Vol 29 (35n36) ◽  
pp. 1530018 ◽  
Author(s):  
J. A. C. Gallas
Keyword(s):  
High Resolution ◽  
Control Parameter ◽  
Chaotic Oscillations ◽  
Periodic Oscillations ◽  
Driven Systems ◽  
Periodically Driven ◽  
Stability Diagrams ◽  
Regular Tiling ◽  
Full Classification

We study the organization of stability phases in the control parameter space of a periodically driven Brusselator. Specifically, we report high-resolution stability diagrams classifying periodic phases in terms of the number of spikes per period of their regular oscillations. Such diagrams contain accumulations of periodic oscillations with an apparently unbounded growth in the number of their spikes. In addition to the entrainment horns, we investigate the organization of oscillations in the limit of small frequencies and amplitudes of the drive. We find this limit to be free from chaotic oscillations and to display an extended and regular tiling of periodic phases. The Brusselator contains also several features discovered recently in more complex scenarios like, e.g. in lasers and in biochemical reactions, and exhibits properties which are helpful in the generic classification of entrainment in driven systems. Our stability diagrams reveal snippets of how the full classification of oscillations might look like for a wide class of flows.

scholarly journals Analytic Signal Depth from High Resolution Aeromagnetic Data over the Gongola Basin Upper Benue Trough Northeastern Nigeria

2021 ◽  
Vol 25 (4) ◽  
pp. 585-590
Author(s):  
H. Musa ◽  
N.E. Bassey ◽  
R. Bello
Keyword(s):  
High Resolution ◽  
Magnetic Structure ◽  
Horizontal Cylinder ◽  
Analytic Signal ◽  
Aeromagnetic Data ◽  
Polynomial Fitting ◽  
Benue Trough ◽  
Local Maxima ◽  
Depth Determination ◽  
Programming Software

The study of high-resolution aeromagnetic data was carried out over the Gongola basin, upper Benue trough, northeastern Nigeria, for analytic signal depth determination. Total intensity magnetic map obtained from the data using the Oasis Montaj TM programming software was used to get the residual map by polynomial fitting, from where the analytic signal was obtained with the use of anomaly width at half the amplitude (X1/2). This was used to carry out depth estimations over the study area. The results showed that it peaks over the magnetic structure with local maxima over its edges (boundaries or contact), and the amplitude is simply related to magnetization, likewise results also showed that the depth estimates were in the range of 1.2 to 5.9 km and were calculated for contact, dyke/sill and horizontal cylinder respectively. The lowest values are from DD profiles, while the highs are from AA profiles. This work is important in identifying dykes, contacts and intrusives over an area.

scholarly journals Discontinuous Spirals of Stable Periodic Oscillations

2013 ◽  
Vol 3 (1) ◽  
Author(s):  
Achim Sack ◽  
Joana G. Freire ◽  
Erik Lindberg ◽  
Thorsten Pöschel ◽  
Jason A. C. Gallas
Keyword(s):  
Periodic Oscillations ◽  
Stable Periodic

ON THE EXISTENCE OF A STABLE PERIODIC SOLUTION OF TWO IMPACTING OSCILLATORS WITH DAMPING

2004 ◽  
Vol 14 (11) ◽  
pp. 3931-3947 ◽  
Author(s):  
KRZYSZTOF CZOLCZYNSKI ◽  
TOMASZ KAPITANIAK
Keyword(s):  
Periodic Solution ◽  
Periodic Motion ◽  
Equations Of Motion ◽  
Analytical Determination ◽  
Stable Periodic Solution ◽  
Numerical Investigations ◽  
Stable Periodic ◽  
Existence Of Periodic Solutions ◽  
The Stability

A system that consists of two impacting oscillators with damping has been considered in this paper. In the first part, a method of analytical determination of the existence of periodic solutions to the equations of motion and a method of analysis of the stability of these solutions are presented. The results of the computations carried out by these methods have been illustrated with a few examples. In the second part of the paper, the results of some numerical investigations are presented. The goal of these studies is to determine, in which regions of parameters characterizing the system, the periodic motion with one impact per period exists and is stable.

Accumulation boundaries: codimension-two accumulation of accumulations in phase diagrams of semiconductor lasers, electric circuits, atmospheric and chemical oscillators

2007 ◽  
Vol 366 (1865) ◽  
pp. 505-517 ◽  
Author(s):  
Cristian Bonatto ◽  
Jason Alfredo Carlson Gallas
Keyword(s):  
Dynamical Systems ◽  
High Resolution ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Phase Diagrams ◽  
Semiconductor Lasers ◽  
Circulation Model ◽  
Electric Circuits ◽  
Chemical Oscillators ◽  
Codimension Two

We report high-resolution phase diagrams for several familiar dynamical systems described by sets of ordinary differential equations: semiconductor lasers; electric circuits; Lorenz-84 low-order atmospheric circulation model; and Rössler and chemical oscillators. All these systems contain chaotic phases with highly complicated and interesting accumulation boundaries , curves where networks of stable islands of regular oscillations with ever-increasing periodicities accumulate systematically. The experimental exploration of such codimension-two boundaries characterized by the presence of infinite accumulation of accumulations is feasible with existing technology for some of these systems.

scholarly journals Chaotic breakdown of a periodically forced, weakly damped pendulum

1992 ◽  
Vol 34 (2) ◽  
pp. 153-173 ◽  
Author(s):  
Peter J. Bryant
Keyword(s):  
Phase Space ◽  
Periodic Solutions ◽  
Initial Conditions ◽  
Period Doubling ◽  
Dimensionless Frequency ◽  
Frequency Range ◽  
Time Intervals ◽  
Maximum Acceleration ◽  
Periodic Oscillations ◽  
Stable Periodic

AbstractAn investigation is made of the transition from periodic solutions through nearly-periodic solutions to chaotic solutions of the differential equation governing forced coplanar motion of a weakly damped pendulum. The pendulum is driven by horizontal, periodic forcing of the pivot with maximum acceleration Є g and dimensionless frequency ω As the forcing frequency ω is decreased gradually at a sufficiently large forcing amplitude Є, it has been shown previously that the pendulum progresses from symmetric oscillations of period T (= 2 π/ω) into a symmetry-breaking, period-doubling sequence of stable, periodic oscillations. There are two related forms of asymmetric, stable oscillations in the sequence, dependent on the initial conditions. When the frequency is decreased immediately beyond the sequence, the oscillations become unstable but remain in the neighbourhood in (θ,) phase space of one or other of the two forms of periodic oscillations, where θ(t) is the pendulum angle with the downward vertical. As the frequency is decreased further, the oscillations move intermittently between the neighbourhoods in (θ,) phase space of each of the two forms of periodic oscillations, in paired nearly-periodic oscillations. Further decrease of the forcing frequency leads to time intervals in which the motion is strongly unstable, with the pendulum passing intermittently over the pivot, interspersed with time intervals when the motion is nearly-periodic and only weakly unstable. The strongly-unstable intervals dominate in fully chaotic oscillations. Windows of independent, stable, periodic oscillations occur throughout the frequency range investigated. It is shown in an appendix how the Floquet method may be interpreted to describe the linear stability of the periodic and nearly-periodic solutions, and the windows of periodic oscillations in the investigated frequency range are listed in a second appendix.

THE STRUCTURE OF INFINITE PERIODIC AND CHAOTIC HUB CASCADES IN PHASE DIAGRAMS OF SIMPLE AUTONOMOUS FLOWS

2010 ◽  
Vol 20 (02) ◽  
pp. 197-211 ◽  
Author(s):  
JASON A. C. GALLAS
Keyword(s):  
Phase Diagrams ◽  
Continuous Time ◽  
Cubic Nonlinearity ◽  
Numerical Investigations ◽  
Chaotic Orbits ◽  
Accumulation Points ◽  
Specific Parameter ◽  
Stable Periodic ◽  
Cubic Polynomial ◽  
Belousov Zhabotinsky Reaction

This manuscript reports numerical investigations about the relative abundance and structure of chaotic phases in autonomous dissipative flows, i.e. in continuous-time dynamical systems described by sets of ordinary differential equations. In the first half, we consider flows containing "periodicity hubs", which are remarkable points responsible for organizing the dynamics regularly over wide parameter regions around them. We describe isolated hubs found in two forms of Rössler's equations and in Chua's circuit, as well as surprising infinite hub cascades that we found in a polynomial chemical flow with a cubic nonlinearity. Hub cascades converge orderly to accumulation points lying on specific parameter paths. In sharp contrast with familiar phenomena associated with unstable orbits, hubs and infinite hub cascades always involve stable periodic and chaotic orbits which are, therefore, directly measurable in experiments. In the last part, we consider flows having no hubs but unusual phase diagrams: a cubic polynomial model containing T-points and wide regions of dense chaos, a nonpolynomial model of the Belousov–Zhabotinsky reaction and the Hindmarsh–Rose model of neuronal bursting, both having chaotic phases with "fountains of chaos". The chaotic regions for the flows discussed here are different from what is known for discrete-time maps. This forcefully shows that knowledge about phase diagrams is quite fragmentary and that much work is still needed to classify and to understand them.

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