I need an example of a critical point of a nonlinear system

Last updated: 8/14/2022

I need an example of a critical point of a nonlinear system of differential equations that satisfy the limit condition for asymptotaclly stable? We know from the definition of asymptotaclly stable critical point that the point must be stable and must satisfy the limit condition (I.e. all the trajectories must approach to the critical point as t goes to infinity), so the limit condition does not mean the asymptotic stability without the fact that the point is stable. I need an example in which the limit condition holds but the critical point is not stable.