HOPF BIFURCATION AND NEW SINGULAR ORBITS COINED IN A LORENZ-LIKE SYSTEM

Haijun Wang; Xianyi Li

doi:10.11948/2018.1307

2018 Volume 8 Issue 5

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Haijun Wang, Xianyi Li. HOPF BIFURCATION AND NEW SINGULAR ORBITS COINED IN A LORENZ-LIKE SYSTEM[J]. Journal of Applied Analysis & Computation, 2018, 8(5): 1307-1325. doi: 10.11948/2018.1307

Citation:

Haijun Wang, Xianyi Li. HOPF BIFURCATION AND NEW SINGULAR ORBITS COINED IN A LORENZ-LIKE SYSTEM[J]. Journal of Applied Analysis & Computation, 2018, 8(5): 1307-1325. doi: 10.11948/2018.1307

HOPF BIFURCATION AND NEW SINGULAR ORBITS COINED IN A LORENZ-LIKE SYSTEM

Institute of Nonlinear Analysis and Department of Big Data Science, School of Science, Zhejiang University of Science and Technology, Hangzhou 310023, China

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Abstract

Abstract

We seize some new dynamics of a Lorenz-like system:ẋ=a(y-x), ẏ=dy -xz, ż=-bz + fx² + gxy, such as for the Hopf bifurcation, the behavior of non-isolated equilibria, the existence of singularly degenerate heteroclinic cycles and homoclinic and heteroclinic orbits. In particular, our new discovery is that the system has also two heteroclinic orbits for bg=2a(f + g) and a > d > 0 other than known bg > 2a(f + g) and a > d > 0, whose proof is completely different from known case. All the theoretical results obtained are also verified by numerical simulations.
- Lorenz-like system /
- singularly degenerate heteroclinic cycle /
- heteroclinic orbit /
- Lyapunov-like function
MSC: 34C37;34D20;37C29

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