Lotka–Volterra equation Competitive Lotka–Volterra equations

2024-05-29 09:59:19

Lotka–Volterra equation

The Lotka–Volterra equations, also known as the predator–prey equations, are a pair of first-order, non-linear, differential equations frequently used to describe the dynamics of biological systems in which two species interact, one as a predator and the other as prey. The populations change through time according to the pair of equations:

where

x is the number of prey (for example, rabbits);
y is the number of some predator (for example, foxes);
and represent the growth rates of the two populations over time;
t represents time; and
, , and are parameters describing the interaction of the two species.

Competitive Lotka–Volterra equations

The competitive Lotka–Volterra equations are a simple model of the population dynamics of species competing for some common resource. They can be furthergeneralised to include trophic interactions.

The form is similar to the Lotka–Volterra equations for predation in that the equation for each species has one term for self-interaction and one term for the interaction with other species. In the equations for predation, the base population model is exponential. For the competition equations, the logistic equationis the basis.

Given two populations, x₁ and x₂, with logistic dynamics, the Lotka–Volterra formulation adds an additional term to account for the species' interactions. Thus the competitive Lotka–Volterra equations are:

Reference:

http://en.wikipedia.org/wiki/Lotka%E2%80%93Volterra_equation

http://en.wikipedia.org/wiki/Competitive_Lotka%E2%80%93Volterra_equations

Lotka–Volterra equation Competitive Lotka–Volterra equations相关推荐

partial equation lecture first order pde lecture 1
核心思想就是尝试尝试出来就成了 reduce differencial equation to the algerbia equations dx/dt=ax assume x=e^(at) m-a ...
一阶线性常微分方程解法总结 Summary of Solving First Order Linear Ordinary Differential Equation (ODE)
文章目录 1. Separable Differentiable Equations 2. Linear Equations First-order linear equation Solution ...
2023年数学建模美赛A题（A drought stricken plant communities）分析与编程
2023年数学建模美赛A题(A drought stricken plant communities)分析与编程 2023年数学建模美赛D题(Prioritizing the UN Sustainab ...
电磁场与电磁波-2-泊松方程、拉普拉斯方程的推导
Derivation of poisson equation and Laplace equation List of used equations Poisson equation Laplace ...
RL(Chapter 3): Finite Markov Decision Processes (有限马尔可夫决策过程)
本文为强化学习笔记,主要参考以下内容: Reinforcement Learning: An Introduction 代码全部来自 GitHub 习题答案参考 Github 目录 The Agent ...
2.2 齐次方程组基础解系
基本解法在线性空间求基的时候,经常会遇到齐次方程组基础解系的问题,比如以下齐次线性方程组: ( 3 2 1 0 0 0 0 0 0 ) v = ( 0 0 0 ) \begin{pmatrix} ...
PHAS0020 Final Assignment
代写PHAS0020作业.代做Python,c/c++,Java程序语言作业.Boundary value作业代写 PHAS0020 Final Assignment 2019 Dr. Christi ...
线性代数提纲整理（大一上）
各位西交利物浦的同学们大家好啊!期末在即,为了不挂科,我费了好大力气,尽自己所能的整理了这些提纲.内容粗浅,如果大家能看到,并且为大家的学习提供了一点点的帮助,那真的再好不过了.哦还有 ...
matlab油气田渗流,基于有限差分的油水兩相渗流方程求解油藏数值模拟毕业设计稿.doc...
基于有限差分的油水兩相渗流方程求解油藏数值模拟毕业设计稿本科毕业设计(论文) 基于有限差分的油水两相渗流方程求解学生姓名: 学号: 专业班级: 指导教师: 2012年 06 月 20 ...
降低神经网络在光纤信道均衡方面的复杂度：从概念到应用
##引言: 尽管基于机器学习,特别是神经网络-NN在光纤传输的均衡上有诸多优势,但是在具体应用上仍有许多的挑战.其中一个重大的挑战是基于NN的经典算法复杂度太高,因此就需要硬件有更快的处理速度和更大的 ...

最新文章

热门文章