Stability of Non-Hyperbolic Equilibrium Point for Polynomial System of Differential Equations

Hadžiabdić, Vahidin; Mehuljić, Midhat; Bektešević, Jasmin

doi:10.18421/tem103-52

Cited by 2 publications

(1 citation statement)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this paper, we use the theory developed in paper [8], [9], [10], and [11]. The study and significance of the ordinary differential equation (ODE) system were in the works [12]- [17] and the discrete system was in the works [5]- [7].…”

Section: Introductionmentioning

confidence: 99%

Dynamics and Bifurcation for One Non-linear System

et al. 2023

View full text Add to dashboard Cite

In this paper, we observed the ordinary differential equation (ODE) system and determined the equilibrium points. To characterize them, we used the existing theory developed to visualize the behavior of the system. We describe the bifurcation that appears, which is characteristic of higher-dimensional systems, that is when a fixed point loses its stability without colliding with other points. Although it is difficult to determine the whole series of bifurcations that lead to chaos, we can say that it is a common opinion that it is precisely the Hopf bifurcation that leads to chaos when it comes to situations that occur in applications. Here, subcritical and supercritical bifurcation occurs, and we can say that subcritical bifurcation represents a much more dramatic situation and is potentially more dangerous than supercritical bifurcation, technically speaking. Namely, bifurcations or trajectories jump to a distant attractor, which can be a fixed point, limit cycle, infinity, or in spaces with three or more dimensions, a foreign attractor.

show abstract