scholarly journals A Stochastic Two Species Competition Model: Nonequilibrium Fluctuation and Stability

2011 ◽  
Vol 2011 ◽  
pp. 1-7 ◽  
Author(s):  
G. P. Samanta
Keyword(s):  
Planck Equation ◽  
Competition Model ◽  
Probability Density Functions ◽  
Density Functions ◽  
Species Competition ◽  
Symmetric Competition ◽  
Competitive Species ◽  
The Stability ◽  
The Relationship ◽  
Nonequilibrium Fluctuation

The object of this paper is to study the stability behaviours of the deterministic and stochastic versions of a two-species symmetric competition model. The logistic parameters of the competitive species are perturbed by colored noises or Ornstein-Uhlenbeck processes due to random environment. The Fokker-Planck equation has been used to obtain probability density functions. Here, we have also discussed the relationship between stability behaviours of this model in a deterministic environment and the corresponding model in a stochastic environment.

Nonholonomic Motion Planning Using Diffusion of Workspace Density Functions

2003 ◽  
Author(s):  
Yu Zhou ◽  
Gregory S. Chirikjian
Keyword(s):  
Planck Equation ◽  
Probability Density Functions ◽  
Time Dependent ◽  
Density Functions ◽  
Value Of Time ◽  
Nonholonomic Mobile Robots ◽  
Planning Algorithm ◽  
The Fourier Transform ◽  
Nonholonomic Motion Planning ◽  
Closed Form Approximation

This paper introduces a trajectory planning algorithm for nonholonomic mobile robots which operate in an environment with obstacles. An important feature of our approach is that the planning domain is the workspace of the mobile robot rather than its configuration space. The basic idea is to imagine the robot being subjected to Brownian motion forcing, and to generate evolving probability density functions (PDF) that describe all attainable positions and orientations of the robot at a given value of time. By planning a path that optimizes the value of this PDF at each instant in time, we generate a feasible trajectory. The PDF of robot pose can be constructed by solving the corresponding Fokker-Planck equation using the Fourier transform for SE(N). A closed-form approximation of the resulting time-dependent PDF is then used to plan a trajectory based on the observation that the evolution of this “workspace density” is a diffusion process. Examples are provided to illustrate the algorithm.

scholarly journals An Extension of Two Species Lotka-Volterra Competition Model

2021 ◽  
Vol 8 (2) ◽  
pp. 90
Author(s):  
Idy BA ◽  
Papa Ibrahima NDIAYE ◽  
Mahe Ndao ◽  
AboubaKary Diakhaby
Keyword(s):  
Global Stability ◽  
Local Stability ◽  
Competition Model ◽  
Complete Analysis ◽  
Species Competition ◽  
Planar System ◽  
Saddle Node Bifurcation ◽  
Competitive Effects ◽  
Competition Effects ◽  
Competitive Species

Limiting resource is a angular stone of the interactions between species in ecosystems such as competition, prey-predators and food chain systems. In this paper, we propose a planar system as an extension of Lotka-Voterra competition model. This describes? two competitive species for a single resource? which are affected by intra and inter-specific interference. We give its complete analysis for the existence and local stability of all equlibria and some conditions of global stability. The model exhibits a rich set of behaviors with a multiplicity of coexistence equilibria, bi-stability, tri-stability and occurrence of global stability of the exclusion of one species and the coexistence? equilibrium. The asymptotic behavior and the number of coexistence equilibria are shown by a saddle-node bifurcation of the level of resource under conditions on competitive effects relatively to associated growth rate per unit of resource.Moreover, we determine the competition outcome in the situations of Balanced and Unbalanced intra-inter species competition effects. Finally, we illustrate results by numerical simulations.

scholarly journals Hopf bifurcation in a reaction-diffusive-advection two-species competition model with one delay

2021 ◽  
pp. 1-24
Author(s):  
Qiong Meng ◽  
Guirong Liu ◽  
Zhen Jin
Keyword(s):  
Steady State ◽  
Hopf Bifurcation ◽  
Competition Model ◽  
Dirichlet Boundary Conditions ◽  
Species Competition ◽  
Normal Form Theory ◽  
Center Manifold Reduction ◽  
Existence And Multiplicity ◽  
The Stability ◽  
Steady State Solutions

In this paper, we investigate a reaction-diffusive-advection two-species competition model with one delay and Dirichlet boundary conditions. The existence and multiplicity of spatially non-homogeneous steady-state solutions are obtained. The stability of spatially nonhomogeneous steady-state solutions and the existence of Hopf bifurcation with the changes of the time delay are obtained by analyzing the distribution of eigenvalues of the infinitesimal generator associated with the linearized system. By the normal form theory and the center manifold reduction, the stability and bifurcation direction of Hopf bifurcating periodic orbits are derived. Finally, numerical simulations are given to illustrate the theoretical results.

scholarly journals Consistency issues in PDF methods

2015 ◽  
Vol 23 (3) ◽  
pp. 187-208
Author(s):  
N. Suciu ◽  
L. Schüler ◽  
S. Attinger ◽  
C. Vamoș ◽  
P. Knabner
Keyword(s):  
Contaminant Transport ◽  
Evolution Equations ◽  
Chemical Species ◽  
Planck Equation ◽  
Probability Density Functions ◽  
Random Environments ◽  
Density Functions ◽  
Ito Process ◽  
Concentration Statistics ◽  
The One

Abstract Concentrations of chemical species transported in random environments need to be statistically characterized by probability density functions (PDF). Solutions to evolution equations for the one-point one-time PDF are usually based on systems of computational particles described by Itô equations. We establish consistency conditions relating the concentration statistics to that of the Itô process and the solution of its associated Fokker-Planck equation to that of the PDF equation. In this frame, we use a recently proposed numerical method which approximates PDFs by particle densities obtained with a global random walk (GRW) algorithm. The GRW-PDF approach is illustrated for a problem of contaminant transport in groundwater.

scholarly journals The Stochastic Stability of Internal HIV Models with Gaussian White Noise and Gaussian Colored Noise

2019 ◽  
Vol 2019 ◽  
pp. 1-8 ◽  
Author(s):  
Xiying Wang ◽  
Yuanxiao Li ◽  
Xiaomei Wang
Keyword(s):  
White Noise ◽  
Probability Density ◽  
Stochastic Stability ◽  
Colored Noise ◽  
Gaussian White Noise ◽  
Probability Density Functions ◽  
Stochastic Dynamic ◽  
Density Functions ◽  
Gaussian Colored Noise ◽  
The Stability

In this paper, the stochastic stability of internal HIV models driven by Gaussian white noise and Gaussian colored noise is analyzed. First, the stability of deterministic models is investigated. By analyzing the characteristic values of endemic equilibrium, we could obtain that internal HIV models reach a steady state under the influence of RTI and PI drugs. Then we discuss the stochastic stability of internal HIV models driven by Gaussian white noise and Gaussian colored noise, based on probability density functions. The functional methods are carried out to derive the approximate Fokker-Planck equation of stochastic internal HIV systems and further obtain the marginal probability density functions. Finally, numerical results show that the noise intensities have a great influence on uninfected cell, infected cell, and virus particles, for predicting the stability of stochastic dynamic systems subjected to Gaussian white noise and Gaussian colored noise.

scholarly journals Time-Dependent Probability Density Functions and Attractor Structure in Self-Organised Shear Flows

Entropy ◽  
2018 ◽  
Vol 20 (8) ◽  
pp. 613 ◽  
Author(s):  
Quentin Jacquet ◽  
Eun-jin Kim ◽  
Rainer Hollerbach
Keyword(s):  
Probability Density ◽  
Shear Flows ◽  
Numerical Solutions ◽  
Planck Equation ◽  
Probability Density Functions ◽  
Time Dependent ◽  
Parameter Study ◽  
Density Functions ◽  
Stochastic Forcing ◽  
Mean Values

We report the time-evolution of Probability Density Functions (PDFs) in a toy model of self-organised shear flows, where the formation of shear flows is induced by a finite memory time of a stochastic forcing, manifested by the emergence of a bimodal PDF with the two peaks representing non-zero mean values of a shear flow. Using theoretical analyses of limiting cases, as well as numerical solutions of the full Fokker–Planck equation, we present a thorough parameter study of PDFs for different values of the correlation time and amplitude of stochastic forcing. From time-dependent PDFs, we calculate the information length ( L ), which is the total number of statistically different states that a system passes through in time and utilise it to understand the information geometry associated with the formation of bimodal or unimodal PDFs. We identify the difference between the relaxation and build-up of the shear gradient in view of information change and discuss the total information length ( L ∞ = L ( t → ∞ ) ) which maps out the underlying attractor structures, highlighting a unique property of L ∞ which depends on the trajectory/history of a PDF’s evolution.

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