Transient and Steady-State Stochastic Analysis of Nonlinear Oscillators Using the Fokker-Planck-Kolmonogrov Equation

2005 ◽  
Author(s):  
Todd Rook
Keyword(s):  
Steady State ◽  
Stochastic Analysis ◽  
Nonlinear Oscillators ◽  
Distribution Functions ◽  
Chaotic Attractors ◽  
Stationary Probability ◽  
Stationary Probability Distribution ◽  
Probability Distribution Functions ◽  
Piecewise Continuous ◽  
Transient And Steady State

An efficient technique to calculate the transient and stationary probability distribution functions (PDF) of the response of SDOF oscillators with piecewise continuous nonlinearities is presented. The method compares favorably with previous methods in reproducing stationary distributions and chaotic attractors, but further work is needed in calculating Lyapunov exponents to the desired accuracy.

STOCHASTIC ANALYSIS FOR THE DESCRIPTION AND SYNTHESIS OF PREDATOR–PREY SYSTEMS

1977 ◽  
Vol 109 (9) ◽  
pp. 1167-1174 ◽  
Author(s):  
Guy L. Curry ◽  
Don W. DeMichele
Keyword(s):  
Steady State ◽  
Mathematical Analysis ◽  
Queueing Theory ◽  
Stochastic Analysis ◽  
Analysis Approach ◽  
Systems Modeling ◽  
Service Facility ◽  
Predator Prey ◽  
System Components ◽  
Transient And Steady State

AbstractIn this paper, a stochastic analysis approach for predator–prey systems modeling is developed. The states of the system are assumed to have a natural probabilistic variation. Elements of queueing theory are used to describe these variations and to obtain both the transient and steady-state results for the system. The predator is considered analogous to a service facility and the prey as customers to be served. The Holling disk equation and mantid–fly experiments are analyzed by this approach. The method provides a framework for a straightforward synthesis of the system components and is readily generalized for multiple predator systems. Furthermore, hunger and other behavioral aspects can be easily incorporated into the mathematical analysis.

STOCHASTIC MODEL CALCULATION FOR THE CARBON MONOXIDE OXIDATION ON IRIDIUM(111) SURFACES

2009 ◽  
Vol 19 (10) ◽  
pp. 3461-3472 ◽  
Author(s):  
JAIME CISTERNAS ◽  
DANIEL ESCAFF ◽  
ORAZIO DESCALZI ◽  
STEFAN WEHNER
Keyword(s):  
Reaction Rate ◽  
External Noise ◽  
Distribution Functions ◽  
Oxidation Of Co ◽  
Stationary Probability Distribution ◽  
Probability Distribution Functions ◽  
First Approximation ◽  
Partial Pressures ◽  
Stochastic Reaction

We study the effect of external noise on the catalytic oxidation of CO on an Iridium(111) single crystal under ultrahigh vacuum conditions. This reaction can be considered as a model of catalysis used in industry. In the absence of noise the reaction exhibits one or two stable stationary states, depending on control parameters such as temperature and partial pressures. When noise is added, for instance, by randomly varying the quality of the influx mixture, the system exhibits stochastic reaction rate and switching. In this work, we present two approaches: one for the monostable regime, and another for the bistable situation that relies on a white noise approximation. Both approaches rest on the assumption that spatial patterns of coverage on the Iridium plate can be neglected on a first approximation. Using mathematical models, it is possible to reconstruct stationary probability distribution functions that match experimental observations and provide support for the existence of a thermodynamic potential.

Extended two-dimensional belief function based on divergence measurement

2020 ◽  
pp. 1-8
Author(s):  
Jianping Fan ◽  
Jing Wang ◽  
Meiqin Wu
Keyword(s):  
Belief Function ◽  
Distribution Functions ◽  
Divergence Measure ◽  
Uncertain Information ◽  
Belief Functions ◽  
Two Dimensional ◽  
Probability Distribution Functions ◽  
Basic Probability ◽  
The Difference ◽  
Supporting Degree

The two-dimensional belief function (TDBF = (mA, mB)) uses a pair of ordered basic probability distribution functions to describe and process uncertain information. Among them, mB includes support degree, non-support degree and reliability unmeasured degree of mA. So it is more abundant and reasonable than the traditional discount coefficient and expresses the evaluation value of experts. However, only considering that the expert’s assessment is single and one-sided, we also need to consider the influence between the belief function itself. The difference in belief function can measure the difference between two belief functions, based on which the supporting degree, non-supporting degree and unmeasured degree of reliability of the evidence are calculated. Based on the divergence measure of belief function, this paper proposes an extended two-dimensional belief function, which can solve some evidence conflict problems and is more objective and better solve a class of problems that TDBF cannot handle. Finally, numerical examples illustrate its effectiveness and rationality.

scholarly journals Development and Evaluation of a Fluctuating Plume Model for Odor Impact Assessment

2021 ◽  
Vol 11 (8) ◽  
pp. 3310
Author(s):  
Marzio Invernizzi ◽  
Federica Capra ◽  
Roberto Sozzi ◽  
Laura Capelli ◽  
Selena Sironi
Keyword(s):  
Experimental Data ◽  
Distribution Functions ◽  
Plume Model ◽  
Probability Distribution Functions ◽  
Weibull Pdf ◽  
Fluctuating Plume ◽  
Concentration Statistics ◽  
Modified Weibull ◽  
Instantaneous Concentration ◽  
Mean Concentration

For environmental odor nuisance, it is extremely important to identify the instantaneous concentration statistics. In this work, a Fluctuating Plume Model for different statistical moments is proposed. It provides data in terms of mean concentrations, variance, and intensity of concentration. The 90th percentile peak-to-mean factor, R90, was tested here by comparing it with the experimental results (Uttenweiler field experiment), considering different Probability Distribution Functions (PDFs): Gamma and the Modified Weibull. Seventy-two percent of the simulated mean concentration values fell within a factor 2 compared to the experimental ones: the model was judged acceptable. Both the modelled results for standard deviation, σC, and concentration intensity, Ic, overestimate the experimental data. This evidence can be due to the non-ideality of the measurement system. The propagation of those errors to the estimation of R90 is complex, but the ranges covered are quite repeatable: the obtained values are 1–3 for the Gamma, 1.5–4 for Modified Weibull PDF, and experimental ones from 1.4 to 3.6.

Modeling of assembly systems with complex structures for throughput analysis during transients

2019 ◽  
Vol 39 (2) ◽  
pp. 262-271
Author(s):  
Yukan Hou ◽  
Yuan Li ◽  
Yuntian Ge ◽  
Jie Zhang ◽  
Shoushan Jiang
Keyword(s):  
Steady State ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Assembly Systems ◽  
Complex Structures ◽  
Throughput Performance ◽  
Throughput Analysis ◽  
Content Type ◽  
Serial Production Lines ◽  
Transient And Steady State

Purpose The purpose of this paper is to present an analytical method for throughput analysis of assembly systems with complex structures during transients. Design/methodology/approach Among the existing studies on the performance evaluation of assembly systems, most focus on the system performance in steady state. Inspired by the transient analysis of serial production lines, the state transition matrix is derived considering the characteristics of merging structure in assembly systems. The system behavior during transients is described by an ergodic Markov chain, with the states being the occupancy of all buffers. The dynamic model for the throughput analysis is solved using the fixed-point theory. Findings This method can be used to predict and evaluate the throughput performance of assembly systems in both transient and steady state. By comparing the model calculation results with the simulation results, this method is proved to be accurate. Originality/value This proposed modeling method can depict the throughput performance of assembly systems in both transient and steady state, whereas most exiting methods can be used for only steady-state analysis. In addition, this method shows the potential for the analysis of complex structured assembly systems owing to the low computational complexity.

Probability Distribution Functions for the Random Forced Burgers Equation

1997 ◽  
Vol 78 (10) ◽  
pp. 1904-1907 ◽  
Author(s):  
Weinan E ◽  
Konstantin Khanin ◽  
Alexandre Mazel ◽  
Yakov Sinai
Keyword(s):  
Probability Distribution ◽  
Burgers Equation ◽  
Distribution Functions ◽  
Probability Distribution Functions
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