definition

For the differential equation $latex \frac{d \mathbf{x}}{dt}=\mathbf{f}(t, \mathbf{x}), \mathbf{x} \in \mathbb{R}^{n}$latexdtdx​=f(t,x),x∈Rn , if $latex \mathbf{f}(t, \tilde{\mathbf{x}})=0$latexf(t,x~)=0 holds for any t, then $latex \tilde{\mathbf{x}}$latexx~ is called the equilibrium point of this differential equation;

For the difference equation $latex x\_{k+1}=\mathbf{f}(t, \mathbf{x}), \mathbf{x\_{k}} \in \mathbb{R}^{n}$latexx_k+1=f(t,x),x_k∈Rn , if $latex \mathbf{f}(k, \tilde{\mathbf{x}})=\tilde{\mathbf{x}}$latexf(k,x~)=x~ holds for $latex k=0,1,2, \ldots$latexk=0,1,2,…, then $latex \tilde{\mathbf{x}}$latexx~ is called the equilibrium point of this difference equation.