Numerical Detection of Stochastic to Deterministic Transition

2014 ◽  
Vol 10 (1) ◽  
Author(s):  
R. K. Brojen Singh
Keyword(s):  
Order Parameter ◽  
System Size ◽  
Limit Cycle Oscillation ◽  
Particle Interactions ◽  
Numerical Estimation ◽  
Noise Parameter ◽  
Chemical Langevin Equation ◽  
Cycle Oscillation ◽  
Random Particle ◽  
Chemical Oscillator

We present the numerical estimation of noise parameter induced in the dynamics of the variables by random particle interactions involved in the stochastic chemical oscillator and use it as order parameter to detect the transition from stochastic to deterministic regime. In stochastic regime, this noise parameter is found to be increased as system size decreases, whereas in deterministic regime it remains constant to minimum value as system size increases. This let the transition from fluctuating to fixed limit cycle oscillation as the system goes from stochastic to deterministic transition. We also numerically estimated the strength of the noise parameter involved both in chemical Langevin equation and Master equation formalisms and found that strength of this parameter is much smaller in the former than the latter.

Dynamics of a delayed competitive system affected by toxic substances with imprecise biological parameters

Filomat ◽  
2017 ◽  
Vol 31 (16) ◽  
pp. 5271-5293
Author(s):  
A.K. Pal ◽  
P. Dolai ◽  
G.P. Samanta
Keyword(s):  
Equilibrium Points ◽  
Stable Limit Cycle ◽  
Limit Cycle Oscillation ◽  
Toxic Substances ◽  
Stable Limit ◽  
Biological Parameters ◽  
Delay Model ◽  
Competitive System ◽  
Interval Numbers ◽  
Cycle Oscillation

In this paper we have studied the dynamical behaviours of a delayed two-species competitive system affected by toxicant with imprecise biological parameters. We have proposed a method to handle these imprecise parameters by using parametric form of interval numbers. We have discussed the existence of various equilibrium points and stability of the system at these equilibrium points. In case of toxic stimulatory system, the delay model exhibits a stable limit cycle oscillation. Computer simulations are carried out to illustrate our analytical findings.

scholarly journals Reducing parametric uncertainty in limit-cycle oscillation computational models

2017 ◽  
Vol 121 (1241) ◽  
pp. 940-969 ◽  
Author(s):  
R. Hayes ◽  
R. Dwight ◽  
S. Marques
Keyword(s):  
Limit Cycle ◽  
Computational Models ◽  
Structural Parameters ◽  
Parametric Uncertainty ◽  
Limit Cycle Oscillation ◽  
Posterior Distributions ◽  
Input Parameters ◽  
Data Points ◽  
Cycle Oscillation ◽  
True Values

ABSTRACTThe assimilation of discrete data points with model predictions can be used to achieve a reduction in the uncertainty of the model input parameters, which generate accurate predictions. The problem investigated here involves the prediction of limit-cycle oscillations using a High-Dimensional Harmonic Balance (HDHB) method. The efficiency of the HDHB method is exploited to enable calibration of structural input parameters using a Bayesian inference technique. Markov-chain Monte Carlo is employed to sample the posterior distributions. Parameter estimation is carried out on a pitch/plunge aerofoil and two Goland wing configurations. In all cases, significant refinement was achieved in the distribution of possible structural parameters allowing better predictions of their true deterministic values. Additionally, a comparison of two approaches to extract the true values from the posterior distributions is presented.

A Harmonic Balance Approach for Modeling Three-Dimensional Nonlinear Unsteady Aerodynamics and Aeroelasticity

2002 ◽  
Author(s):  
Jeffrey P. Thomas ◽  
Earl H. Dowell ◽  
Kenneth C. Hall
Keyword(s):  
Limit Cycle ◽  
Harmonic Balance ◽  
Structural Model ◽  
Oscillation Amplitude ◽  
Three Dimensional ◽  
Unsteady Aerodynamics ◽  
Finite Amplitude ◽  
Limit Cycle Oscillation ◽  
Unsteady Aerodynamic ◽  
Cycle Oscillation

Presented is a frequency domain harmonic balance (HB) technique for modeling nonlinear unsteady aerodynamics of three-dimensional transonic inviscid flows about wing configurations. The method can be used to model efficiently nonlinear unsteady aerodynamic forces due to finite amplitude motions of a prescribed unsteady oscillation frequency. When combined with a suitable structural model, aeroelastic (fluid-structure), analyses may be performed at a greatly reduced cost relative to time marching methods to determine the limit cycle oscillations (LCO) that may arise. As a demonstration of the method, nonlinear unsteady aerodynamic response and limit cycle oscillation trends are presented for the AGARD 445.6 wing configuration. Computational results based on the inviscid flow model indicate that the AGARD 445.6 wing configuration exhibits only mildly nonlinear unsteady aerodynamic effects for relatively large amplitude motions. Furthermore, and most likely a consequence of the observed mild nonlinear aerodynamic behavior, the aeroelastic limit cycle oscillation amplitude is predicted to increase rapidly for reduced velocities beyond the flutter boundary. This is consistent with results from other time-domain calculations. Although not a configuration that exhibits strong LCO characteristics, the AGARD 445.6 wing nonetheless serves as an excellent example for demonstrating the HB/LCO solution procedure.

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