scholarly journals Deterministic and Stochastic Research of Cubic Population Model with Harvesting

2021 ◽  
pp. 2150023
Author(s):  
Özgür Gültekin ◽  
Çağatay Eskin ◽  
Esra Yazicioğlu
Keyword(s):  
Langevin Equation ◽  
Allee Effect ◽  
Deterministic Model ◽  
Probability Distributions ◽  
Gaussian White Noise ◽  
Quadratic Function ◽  
Planck Equation ◽  
Detailed Examination ◽  
Fokker Planck Equation ◽  
Fokker Planck

A detailed examination of the effect of harvesting on a population has been carried out by extending the standard cubic deterministic model by considering a population under Allee effect with a quadratic function representing harvesting. Weak and strong Allee effect transitions, carrying capacity, and Allee threshold change according to harvesting are first discussed in the deterministic model. A Fokker–Planck equation has been obtained starting from a Langevin equation subject to correlated Gaussian white noise with zero mean, and an Approximate Fokker–Planck Equation has been obtained from a Langevin equation subject to correlated Gaussian colored noise with zero mean. This allowed to calculate the stationary probability distributions of populations, and thus to discuss the effects of linear and nonlinear (Holling type-II) harvesting for populations under Allee effect and subject to white and colored noises, respectively.

Approximate Solution of the Fokker–Planck Equation for a Multidegree of Freedom Frictionally Damped Bladed Disk Under Random Excitation

2018 ◽  
Vol 141 (1) ◽  
Author(s):  
Alwin Förster ◽  
Lars Panning-von Scheidt ◽  
Jörg Wallaschek
Keyword(s):  
Approximate Solution ◽  
Weighting Function ◽  
Gaussian White Noise ◽  
Planck Equation ◽  
Random Excitation ◽  
Stationary Response ◽  
Bladed Disk ◽  
Fokker Planck Equation ◽  
Finite Differences Method ◽  
Fokker Planck

Bladed disks are subjected to different types of excitations, which cannot, in any, case be described in a deterministic manner. Fuzzy factors, such as slightly varying airflow or density fluctuation, can lead to an uncertain excitation in terms of amplitude and frequency, which has to be described by random variables. The computation of frictionally damped blades under random excitation becomes highly complex due to the presence of nonlinearities. Only a few publications are dedicated to this particular problem. Most of these deal with systems of only one or two degrees-of-freedom (DOFs) and use computational expensive methods, like finite element method or finite differences method (FDM), to solve the determining differential equation. The stochastic stationary response of a mechanical system is characterized by the joint probability density function (JPDF), which is driven by the Fokker–Planck equation (FPE). Exact stationary solutions of the FPE only exist for a few classes of mechanical systems. This paper presents the application of a semi-analytical Galerkin-type method to a frictionally damped bladed disk under influence of Gaussian white noise (GWN) excitation in order to calculate its stationary response. One of the main difficulties is the selection of a proper initial approximate solution, which is applicable as a weighting function. Comparing the presented results with those from the FDM, Monte–Carlo simulation (MCS) as well as analytical solutions proves the applicability of the methodology.

scholarly journals GENERALIZED WIENER PROCESS AND KOLMOGOROV'S EQUATION FOR DIFFUSION INDUCED BY NON-GAUSSIAN NOISE SOURCE

2005 ◽  
Vol 05 (02) ◽  
pp. L267-L274 ◽  
Author(s):  
ALEXANDER DUBKOV ◽  
BERNARDO SPAGNOLO
Keyword(s):  
White Noise ◽  
Wiener Process ◽  
Anomalous Diffusion ◽  
Gaussian Noise ◽  
Gaussian White Noise ◽  
Planck Equation ◽  
Fokker Planck Equation ◽  
Non Gaussian ◽  
Generalized Wiener Process ◽  
Fokker Planck

We show that the increments of generalized Wiener process, useful to describe non-Gaussian white noise sources, have the properties of infinitely divisible random processes. Using functional approach and the new correlation formula for non-Gaussian white noise we derive directly from Langevin equation, with such a random source, the Kolmogorov's equation for Markovian non-Gaussian process. From this equation we obtain the Fokker–Planck equation for nonlinear system driven by white Gaussian noise, the Kolmogorov–Feller equation for discontinuous Markovian processes, and the fractional Fokker–Planck equation for anomalous diffusion. The stationary probability distributions for some simple cases of anomalous diffusion are derived.

Approximate Solution of the Fokker-Planck Equation for a Multi-Degree of Freedom Frictionally Damped Bladed Disk Under Random Excitation

2018 ◽  
Author(s):  
Alwin Förster ◽  
Lars Panning-von Scheidt ◽  
Jörg Wallaschek
Keyword(s):  
Approximate Solution ◽  
Weighting Function ◽  
Gaussian White Noise ◽  
Planck Equation ◽  
Random Excitation ◽  
Stationary Response ◽  
Bladed Disk ◽  
Fokker Planck Equation ◽  
Finite Differences Method ◽  
Fokker Planck

Bladed Disks are subjected to different types of excitations, which cannot in any case be described in a deterministic manner. Fuzzy factors, such as slightly varying airflow or density fluctuation, can lead to an uncertain excitation in terms of amplitude and frequency, which has to be described by random variables. The computation of frictionally damped blades under random excitation becomes highly complex due to the presence of nonlinearities. Only a few publications are dedicated to this particular problem. Most of these deal with systems of only one or two degrees of freedom and use computational expensive methods, like finite element method (FEM) or finite differences method (FDM), to solve the determining differential equation. The stochastic stationary response of a mechanical system is characterized by the joint probability density function (JPDF), which is driven by the Fokker-Planck equation (FPE). Exact stationary solutions of the FPE only exist for a few classes of mechanical systems. This paper presents the application of a semi-analytical Galerkin-type method to a frictionally damped bladed disk under influence of Gaussian white noise (GWN) excitation in order to calculate its stationary response. One of the main difficulties is the selection of a proper initial approximate solution, which is applicable as a weighting function. Comparing the presented results with those from the FDM, Monte-Carlo Simulation (MCS) as well as analytical solutions proves the applicability of the methodology.

PARITY-VIOLATING ANOMALY FROM THE FOKKER-PLANCK EQUATION

1991 ◽  
Vol 06 (02) ◽  
pp. 123-128
Author(s):  
G. NARDULLI ◽  
L. TEDESCO
Keyword(s):  
Langevin Equation ◽  
Gauge Theories ◽  
Planck Equation ◽  
Quantization Scheme ◽  
Stochastic Quantization ◽  
Fokker Planck Equation ◽  
Fokker Planck

We compute parity-violating anomaly in gauge theories with odd number of dimensions using an approach based on the effective Fokker-Planck equation in the stochastic quantization scheme. We find results that agree with those obtained by the Langevin equation.

STOCHASTIC CALCULUS AND COVARIANT AND ROTATION-INVARIANT LANGEVIN EQUATION FOR GRAVITY

1990 ◽  
Vol 05 (28) ◽  
pp. 2335-2342 ◽  
Author(s):  
RIUJI MOCHIZUKI
Keyword(s):  
Langevin Equation ◽  
Planck Equation ◽  
Stochastic Calculus ◽  
Rotation Invariant ◽  
Fokker Planck Equation ◽  
Fokker Planck

We investigate the relations among the Langevin equation, the Fokker-Planck equation, and the stochastic action, both in the sense of Ito and of Stratonovich. In the latter case we suggest a somewhat modified Langevin equation which is covariant and rotation-invariant.

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