Transient probability in basins of noise influenced responses of mono and coupled Duffing oscillators

2021 ◽  
Vol 31 (6) ◽  
pp. 063117
Author(s):  
Lautaro Cilenti ◽  
Balakumar Balachandran
Keyword(s):  
Coupled Duffing Oscillators ◽  
Transient Probability

Analysis of transient behaviour of certain processes with return to a central state

1983 ◽  
Vol 20 (01) ◽  
pp. 61-70
Author(s):  
Peter G. Buckholtz ◽  
L. Lorne Campbell ◽  
Ross D. Milbourne ◽  
M. T. Wasan
Keyword(s):  
Probability Distribution ◽  
Diffusion Equation ◽  
Diffusion Approximation ◽  
Cash Management ◽  
Central State ◽  
Transient Behaviour ◽  
Management Problems ◽  
Transient Probability ◽  
Birth Death

In economics, cash management problems may be modelled by birth-death processes which reset to central states when a boundary is reached. The nature of the transient behaviour of the probability distribution of such processes symmetric about a central state is investigated. A diffusion approximation of such processes is given and the transient probability behaviour derived from the diffusion equation.

scholarly journals NON-LINEAR DYNAMICS, ENTANGLEMENT AND THE QUANTUM-CLASSICAL CROSSOVER OF TWO COUPLED SQUID RINGS

2009 ◽  
Vol 23 (20n21) ◽  
pp. 4311-4319
Author(s):  
M. J. EVERITT
Keyword(s):  
Classical Limit ◽  
Quantum Interference ◽  
Superconducting Quantum Interference Device ◽  
Similar System ◽  
Linear Dynamics ◽  
Superconducting Quantum Interference ◽  
Non Linear ◽  
Two Systems ◽  
Coupled Duffing Oscillators ◽  
Squid Rings

We explore the quantum-classical crossover of two coupled, identical, superconducting quantum interference device (SQUID) rings. We note that the motivation for this work is based on a study of a similar system comprising two coupled Duffing oscillators. In that work we showed that the entanglement characteristics of chaotic and periodic (entrained) solutions differed significantly and that in the classical limit entanglement was preserved only in the chaotic-like solutions. However, Duffing oscillators are a highly idealised toy model. Motivated by a wish to explore more experimentally realisable systems we now extend our work to an analysis of two coupled SQUID rings. We observe some differences in behaviour between the system that is based on SQUID rings rather than on Duffing oscillators. However, we show that the two systems share a common feature. That is, even when the SQUID ring's trajectories appear to follow (semi) classical orbits entanglement persists.

scholarly journals Stability of the 3-torus solution in a ring of coupled Duffing oscillators

2020 ◽  
Vol 229 (12-13) ◽  
pp. 2249-2259
Author(s):  
L. Borkowski ◽  
A. Stefanski
Keyword(s):  
Numerical Simulation ◽  
Wave Flow ◽  
Wide Range ◽  
Single Well ◽  
Rotating Wave ◽  
Independent Effects ◽  
Coupled Duffing Oscillators

Abstract The dynamics of the ring of unidirectionally coupled single-well Duffing oscillators is analyzed in numerical simulation for identical nodal oscillators. The research is concentrated on the existence of the stable 3D torus attractor in this system. It is shown that 3-frequency quasi-periodicity can be robustly stable in wide range of parameters of the system under consideration. As an explanation of this stability, the conjecture on the coexistence and superposition of two independent effects characterized with irrational frequencies, i.e., the classical Newhouse, Ruelle and Takens scenario and rotating wave flow, is formulated.

On the transient behavior of the repairman problem

1991 ◽  
Vol 23 (02) ◽  
pp. 327-354 ◽  
Author(s):  
Charles Knessl
Keyword(s):  
Finite Population ◽  
Transient Behavior ◽  
Boundary Layer Theory ◽  
Asymptotic Approximations ◽  
Perturbation Techniques ◽  
Ray Method ◽  
Repair Rate ◽  
Repairman Problem ◽  
Transient Probability

We consider the repairman problem which corresponds to the finite population M/M/1 queue. Asymptotic approximations for the transient probability distribution of the number of broken machines constructed when the number M of machines is large and the service (repair) rate is also large, specifically, O(M). The approximations are constructed by using singular perturbation techniques such as the ray method, boundary layer theory, and the method of matched asymptotic expansions. Extensive numerical comparisons show the quality of our approximations.

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