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

Haijun Wang | Zendy; Xianyi Li | Zendy

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

Author(s) -

Haijun Wang,

Xianyi Li

Publication year - 2018

Publication title -

journal of applied analysis and computation

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.55

H-Index - 21

eISSN - 2158-5644

pISSN - 2156-907X

DOI - 10.11948/2018.1307

Subject(s) - heteroclinic bifurcation , heteroclinic cycle , homoclinic orbit , heteroclinic orbit , bogdanov–takens bifurcation , degenerate energy levels , mathematics , hopf bifurcation , homoclinic bifurcation , bifurcation , mathematical analysis , pure mathematics , physics , nonlinear system , quantum mechanics

We seize some new dynamics of a Lorenz-like system: ẋ = a(y−x), ẏ = dy − xz, ż = −bz + fx + 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.

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