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Modeling, dynamical analysis and numerical simulation of a new 3D cubic Lorenz-like system.
- Source :
- Scientific Reports; 4/24/2023, Vol. 13 Issue 1, p1-15, 15p
- Publication Year :
- 2023
-
Abstract
- Little seems to be considered about the globally exponentially asymptotical stability of parabolic type equilibria and the existence of heteroclinic orbits in the Lorenz-like system with high-order nonlinear terms. To achieve this target, by adding the nonlinear terms yz and x 2 y to the second equation of the system, this paper introduces the new 3D cubic Lorenz-like system: x ˙ = a (y - x) , y ˙ = b 1 y + b 2 y z + b 3 x z + b 4 x 2 y , z ˙ = - c z + y 2 , which does not belong to the generalized Lorenz systems family. In addition to giving rise to generic and degenerate pitchfork bifurcation, Hopf bifurcation, hidden Lorenz-like attractors, singularly degenerate heteroclinic cycles with nearby chaotic attractors, etc., one still rigorously proves that not only the parabolic type equilibria S x = { (x , x , x 2 c) | x ∈ R , c ≠ 0 } are globally exponentially asymptotically stable, but also there exists a pair of symmetrical heteroclinic orbits with respect to the z-axis, as most other Lorenz-like systems. This study may offer new insights into revealing some other novel dynamic characteristics of the Lorenz-like system family. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 20452322
- Volume :
- 13
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- Scientific Reports
- Publication Type :
- Academic Journal
- Accession number :
- 163294944
- Full Text :
- https://doi.org/10.1038/s41598-023-33826-4