@Rouben Rostamian   I called it nonlinear due to the fact that on the right side there is a nonstationary component that changes in time. As for the article - judging by its title, it solves the problem, but my level of knowledge is not enough to understand it and try to calculate something. I need help here. Let's summarize briefly: there is a right-hand side with components that make the system non-autonomous. Despite the fact that there is no equilibrium point as such, but there is movement around this point, you can try to remove this nonlinear component by linearization, leaving only the most essential properties of the transient process.

@Preben Alsholm  I'm not interested in a numerical solution. I want to identify the most significant properties of the transient process. Neglecting oscillations around a stationary point, it is necessary to describe linearly (albeit roughly) the transition from the initial position to the final one. How to linearize such a system?

@Preben Alsholm  So that's understandable. It's not about that at all, but about how to linearize. Look here. The stationary point is essentially not there. The system vibrates around. We can say that it is quasi-stationary. Nevertheless, the system passes from the initial state to the final one with some dynamics quite similar to the linear one. The main parameters of this dynamics must be estimated by linearizing the differential equation. Help me to do this.  https://www.sciencedirect.com/science/article/pii/S0007449714001006

@Carl Love 

x__||(1..4)||0  - anything you want