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- Community_matrix abstract "In mathematical biology, the community matrix is the linearization of the Lotka–Volterra equation at an equilibrium point. The eigenvalues of the community matrix determine the stability of the equilibrium point.The Lotka–Volterra predator-prey model iswhere x(t) denotes the number of prey, y(t) the number of predators, and α, β, γ and δ are constants. The linearization of these differential equations at an equilibrium point (x*, y*) has the formwhere u = x − x* and v = y − y*. The matrix A is called the community matrix. If A has an eigenvalue with positive real part then the equilibrium is unstable, but if all eigenvalues have negative real part then it is stable.".
- Community_matrix wikiPageID "22174129".
- Community_matrix wikiPageRevisionID "594398403".
- Community_matrix hasPhotoCollection Community_matrix.
- Community_matrix subject Category:Dynamical_systems.
- Community_matrix subject Category:Mathematical_and_theoretical_biology.
- Community_matrix subject Category:Population_ecology.
- Community_matrix type Abstraction100002137.
- Community_matrix type Attribute100024264.
- Community_matrix type DynamicalSystem106246361.
- Community_matrix type DynamicalSystems.
- Community_matrix type PhaseSpace100029114.
- Community_matrix type Space100028651.
- Community_matrix comment "In mathematical biology, the community matrix is the linearization of the Lotka–Volterra equation at an equilibrium point. The eigenvalues of the community matrix determine the stability of the equilibrium point.The Lotka–Volterra predator-prey model iswhere x(t) denotes the number of prey, y(t) the number of predators, and α, β, γ and δ are constants. The linearization of these differential equations at an equilibrium point (x*, y*) has the formwhere u = x − x* and v = y − y*.".
- Community_matrix label "Community matrix".
- Community_matrix sameAs m.05q95ch.
- Community_matrix sameAs Q5154984.
- Community_matrix sameAs Q5154984.
- Community_matrix sameAs Community_matrix.
- Community_matrix wasDerivedFrom Community_matrix?oldid=594398403.
- Community_matrix isPrimaryTopicOf Community_matrix.