Systems and stability

Concepts

• Eigenvalue and eigenvector from Linear algebra 10 exercisesAn eigenvector v of a square matrix A is a nonzero vector that A only stretches, shrinks or flips, without taking it off its line…
• System of differential equations 10 exercisesA set of n equations that fix, through a vector function mathbf F, the derivatives of n unknown functions x_1(t),dots,x_n(t) of a…
• Linear system and eigenvalues 10 exercisesHomogeneous system with a constant n× n matrix A, whose elementary solutions are built from an eigenvalue λ and an eigenvector ma…
• Phase plane 10 exercisesCoordinate plane (x,y) of an autonomous system whose velocities f and g do not depend on t; each solution is drawn there as a cur…
• Stability of an equilibrium 10 exercisesAn equilibrium mathbf x^* is stable if, for every tolerance ε, there is a radius δ such that solutions starting within δ of it ne…