{"type":"rich","version":"1.0","title":"Linearisation about an equilibrium and the eigenvalue stability criterion","html":"<span class=\"wb-embed wb-embed-math\" data-latex=\"\\mathbf{u}'=A\\mathbf{u},\\qquad A=D\\mathbf{f}(\\mathbf{x}^{*});\\qquad \\operatorname{Re}(\\lambda)<0\\ \\text{for all eigenvalues } \\lambda\\ \\Rightarrow\\ \\mathbf{x}^{*}\\ \\text{asymptotically stable}\">\\mathbf{u}'=A\\mathbf{u},\\qquad A=D\\mathbf{f}(\\mathbf{x}^{*});\\qquad \\operatorname{Re}(\\lambda)&lt;0\\ \\text{for all eigenvalues } \\lambda\\ \\Rightarrow\\ \\mathbf{x}^{*}\\ \\text{asymptotically stable}</span>","width":640,"height":320}