A dynamical system with no equilibrium points is categorized as chaotic system(in which case the evolution of any two distinct points of the attractor result in exponentially diverging trajectories, which complicates prediction when even the smallest noise is present in the system.) Lorenzian chaos, "sandwich" chaos, and "horseshoe" chaos. with hidden attraction(It is an "attractor" because it attracts solutions (so solutions eventually become as complicated as the attractor), and it is "strange" because it has a fractal structure, and so is infinitely complicated.) because the loss of equilibrium points means that its basin of attraction does not intersect with small neighborhoods of any equilibrium points.The output value y0 corresponding to the equilibrium point (x0, u0) can be directly determined using the output equation: y0 = g(x0,u0). For nonlinear systems the stability is NOT a global property of the system, but a “local” property of the considered equilibrium point x0. Non-equilibrium systems require a continuous input of energy to retain their functional state, which makes for a fundamental difference to systems that operate at thermodynamic equilibrium. Kinetic asymmetry in the energy consumption pathway is required to drive systems out of equilibrium.

https://www.hindawi.com/journals/jndy/2015/257923/