Lotka–Volterra equations (Q7970): Difference between revisions

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first-order nonlinear 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

Lotka-Volterra equation
predator–prey equation

Language	Label	Description	Also known as
English	Lotka–Volterra equations	first-order nonlinear 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	Lotka-Volterra equation predator–prey equation

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{\begin{aligned}{\frac {\mathrm {d} x}{\mathrm {d} t}}&=\alpha x-\beta xy\\{\frac {\mathrm {d} y}{\mathrm {d} t}}&=\delta xy-\gamma y\end{aligned}}

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Revision as of 11:29, 1 May 2023 Fire (talk \| contribs) Bureaucrats, Interface administrators, Administrators 132,738 edits ‎Created claim: subclass of (P1): Kolmogorov equations (Q7971) ← Older edit	Revision as of 11:30, 1 May 2023 Fire (talk \| contribs) Bureaucrats, Interface administrators, Administrators 132,738 edits ‎Created claim: defining formula (P333): \begin{aligned}\frac{\mathrm dx}{\mathrm dt}&=\alpha x-\beta xy\\\frac{\mathrm dy}{\mathrm dt}&=\delta xy-\gamma y\end{aligned} Newer edit →
	Property / defining formula
		${\begin{aligned}{\frac {\mathrm {d} x}{\mathrm {d} t}}&=\alpha x-\beta xy\\{\frac {\mathrm {d} y}{\mathrm {d} t}}&=\delta xy-\gamma y\end{aligned}}$ `\begin{aligned}\frac{\mathrm dx}{\mathrm dt}&=\alpha x-\beta xy\\\frac{\mathrm dy}{\mathrm dt}&=\delta xy-\gamma y\end{aligned}`
	Property / defining formula: ${\begin{aligned}{\frac {\mathrm {d} x}{\mathrm {d} t}}&=\alpha x-\beta xy\\{\frac {\mathrm {d} y}{\mathrm {d} t}}&=\delta xy-\gamma y\end{aligned}}$ / rank
		Normal rank

Lotka–Volterra equations (Q7970): Difference between revisions

${\begin{aligned}{\frac {\mathrm {d} x}{\mathrm {d} t}}&=\alpha x-\beta xy\\{\frac {\mathrm {d} y}{\mathrm {d} t}}&=\delta xy-\gamma y\end{aligned}}$

Revision as of 11:30, 1 May 2023

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Lotka–Volterra equations (Q7970): Difference between revisions

d x d t = α x − β x y d y d t = δ x y − γ y {\displaystyle {\begin{aligned}{\frac {\mathrm {d} x}{\mathrm {d} t}}&=\alpha x-\beta xy\\{\frac {\mathrm {d} y}{\mathrm {d} t}}&=\delta xy-\gamma y\end{aligned}}}

Revision as of 11:30, 1 May 2023

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${\begin{aligned}{\frac {\mathrm {d} x}{\mathrm {d} t}}&=\alpha x-\beta xy\\{\frac {\mathrm {d} y}{\mathrm {d} t}}&=\delta xy-\gamma y\end{aligned}}$