Science, Engineering and Technology (Jan 2022)
Dynamics and bifurcation for one non-linear system
Abstract
In this paper, we will observe the ODE system, determine the equilibrium points. To characterize them, using the theory developed so far, to visualize the behavior of the system. Describe the bifurcation that appears, which is characteristic of higher dimensional systems, i.e. when a fixed point loses stability without colliding with other points. Although it is very difficult to determine the complete series of bifurcations that lead to chaos, we can say that it is a well-established opinion that it is precisely the Hopf bifurcation that leads to it, when it comes to situations that occur in applications. Subcritical and supercritical bifurcation occur here, we can say that subcritical bifurcation represents a much more dramatic situation and potentially more dangerous than supercritical, in technique. Namely, bifurcations, or trajectories, jump to a distant attractor, which can be a fixed point, a limit cycle, infinity, or in spaces with three or more dimensions, a foreign attractor.
