Break-Even Point/BEP

definition

For the differential equation $latex \frac{d \mathbf{x}}{dt}=\mathbf{f}(t, \mathbf{x}), \mathbf{x} \in \mathbb{R}^{n}$ , if $latex \mathbf{f}(t, \tilde{\mathbf{x}})=0$ holds for any t, then $latex \tilde{\mathbf{x}}$ 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} $ , if $latex \mathbf{f}(k, \tilde{\mathbf{x}})=\tilde{\mathbf{x}} $ holds for $latex k=0,1,2, \ldots $, then $latex \tilde{\mathbf{x}}$ is called the equilibrium point of this difference equation.