Algebraic Dynamical Approach to the su(1,1)[Formula: see text]h(3) Dynamical System: A Generalized Harmonic Oscillator in an External Field

1997 ◽  
Vol 7 (6) ◽  
pp. 749-758 ◽  
Author(s):  
W. Zuo ◽  
S. J. Wang
Keyword(s):  
Dynamical System ◽  
External Field ◽  
Harmonic Oscillator ◽  
Dynamical Approach ◽  
System A ◽  
Generalized Harmonic Oscillator

scholarly journals Inverse-square law between time and amplitude for crossing tipping thresholds

2019 ◽  
Vol 475 (2222) ◽  
pp. 20180504 ◽  
Author(s):  
Paul Ritchie ◽  
Özkan Karabacak ◽  
Jan Sieber
Keyword(s):  
Dynamical System ◽  
Feedback Loop ◽  
Tipping Point ◽  
Dimensional System ◽  
Stochastic Forcing ◽  
Inverse Square Law ◽  
System A ◽  
Asymptotic Expressions ◽  
Higher Dimensional ◽  
Random Disturbances

A classical scenario for tipping is that a dynamical system experiences a slow parameter drift across a fold tipping point, caused by a run-away positive feedback loop. We study what happens if one turns around after one has crossed the threshold. We derive a simple criterion that relates how far the parameter exceeds the tipping threshold maximally and how long the parameter stays above the threshold to avoid tipping in an inverse-square law to observable properties of the dynamical system near the fold. For the case when the dynamical system is subject to stochastic forcing we give an approximation to the probability of tipping if a parameter changing in time reverses near the tipping point. The derived approximations are valid if the parameter change in time is sufficiently slow. We demonstrate for a higher-dimensional system, a model for the Indian summer monsoon, how numerically observed escape from the equilibrium converge to our asymptotic expressions. The inverse-square law between peak of the parameter forcing and the time the parameter spends above a given threshold is also visible in the level curves of equal probability when the system is subject to random disturbances.

Sampling time scheduling for a CAN-based dynamical system: A simulation practice

2015 ◽  
Author(s):  
Amira Sarayati Ahmad Dahalan ◽  
Abdul Rashid Husaint ◽  
Mohd Badril NorShah ◽  
Muhammad Iqbal Zakaria ◽  
Muhammad Nizam Kamarudin
Keyword(s):  
Dynamical System ◽  
Sampling Time ◽  
System A ◽  
Time Scheduling ◽  
Simulation Practice

Naïve Bayes switching linear dynamical system: A model for dynamic system modelling, classification, and information fusion

2018 ◽  
Vol 42 ◽  
pp. 75-101 ◽  
Author(s):  
Joel Janek Dabrowski ◽  
Johan Pieter de Villiers ◽  
Conrad Beyers
Keyword(s):  
Dynamical System ◽  
Dynamic System ◽  
Information Fusion ◽  
Naive Bayes ◽  
Naïve Bayes ◽  
System Modelling ◽  
Linear Dynamical System ◽  
System A

Quantum mechanical bound rotator as a generalized harmonic oscillator

1994 ◽  
Vol 6 (47) ◽  
pp. 10297-10306 ◽  
Author(s):  
S Raghavan ◽  
V M Kenkre
Keyword(s):  
Harmonic Oscillator ◽  
Quantum Mechanical ◽  
Generalized Harmonic Oscillator

scholarly journals Extending Characters of Fixed Point Algebras

Axioms ◽  
2018 ◽  
Vol 7 (4) ◽  
pp. 79
Author(s):  
Stefan Wagner
Keyword(s):  
Dynamical System ◽  
Fixed Point ◽  
Topological Group ◽  
Continuous Action ◽  
Group Of Units ◽  
System A ◽  
Fixed Point Algebra ◽  
Continuous Inverse ◽  
Locally Convex ◽  
Locally Convex Algebra

A dynamical system is a triple ( A , G , α ) consisting of a unital locally convex algebra A, a topological group G, and a group homomorphism α : G → Aut ( A ) that induces a continuous action of G on A. Furthermore, a unital locally convex algebra A is called a continuous inverse algebra, or CIA for short, if its group of units A × is open in A and the inversion map ι : A × → A × , a ↦ a − 1 is continuous at 1 A . Given a dynamical system ( A , G , α ) with a complete commutative CIA A and a compact group G, we show that each character of the corresponding fixed point algebra can be extended to a character of A.

Dynamical system approach to cosmological evolution in modified theories of gravity with coupling between matter and geometry

2020 ◽  
Vol 35 (19) ◽  
pp. 2050154
Author(s):  
Jun Wang ◽  
Kang Liu
Keyword(s):  
Dynamical System ◽  
System Approach ◽  
Cosmic Radiation ◽  
Cosmological Evolution ◽  
Accelerated Expansion ◽  
Modified Theories Of Gravity ◽  
Late Time ◽  
Dynamical System Approach ◽  
Dynamical Approach ◽  
Theories Of Gravity

In this paper, a class of [Formula: see text] gravitational models with coupling between matter and geometry have been studied by a dynamical approach in cosmology. The result shows that both the cosmic radiation dominated era and the late-time cosmic accelerated expansion can be achieved in this class of models. Moreover, the corresponding parameters are constrained as well.

scholarly journals Regular and Chaotic Motion in a Restricted Three–Body Problem of Astrophysical Interest

2000 ◽  
Vol 174 ◽  
pp. 281-285 ◽  
Author(s):  
J. C. Muzzio ◽  
F. C. Wachlin ◽  
D. D. Carpintero
Keyword(s):  
External Field ◽  
Body Problem ◽  
Stellar System ◽  
Three Dimensional ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Stellar Orbits ◽  
System A ◽  
Regular And Chaotic Motion ◽  
Three Body

AbstractWe have studied the motion of massless particles (stars) bound to a stellar system (a galactic satellite) that moves on a circular orbit in an external field (a galaxy). A large percentage of the stellar orbits turned out to be chaotic, contrary to what happens in the usual restricted three–body problem of celestial mechanics where most of the orbits are regular. The discrepancy is probably due to three facts: 1) Our study is not limited to orbits on the main planes of symmetry, but considers three–dimensional motion; 2) The force exerted by the satellite goes to zero (rather than to infinity) at the center of the satellite; 3) The potential of the satellite is triaxial, rather than spherical.

scholarly journals Constructing the time independent Hamiltonian from a time dependent one

Open Physics ◽  
2007 ◽  
Vol 5 (3) ◽  
Author(s):  
Michał Dobrski
Keyword(s):  
Dynamical System ◽  
Harmonic Oscillator ◽  
Time Dependent ◽  
Damped Harmonic Oscillator ◽  
Hamiltonian Dynamical System ◽  
Equivalent Time ◽  
New Time

AbstractIn this paper we introduce a method for finding a time independent Hamiltonian of a given Hamiltonian dynamical system by canonoid transformation of canonical momenta. We find a condition that the system should satisfy to have an equivalent time independent formulation. We study the example of a damped harmonic oscillator and give the new time independent Hamiltonian for it, which has the property of tending to the standard Hamiltonian of the harmonic oscillator as damping goes to zero.

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