Multitudinous potential homoclinic and heteroclinic orbits seized

Abstract

Revisiting a newly reported modified Chen system by both the definitions of $ \alpha $-limit and $ \omega $-limit set, Lyapunov function and Hamiltonian function, this paper seized a multitude of pairs of potential heteroclinic orbits to (1) $ E_{0} $ and $ E_{\pm} $, or (2) $ E_{+} $ or (3) $ E_{-} $, and homoclinic and heteroclinic orbits on its invariant algebraic surface $ Q = z - \frac{x^{2}}{2a} = 0 $ with cofactor $ -2a $, which is not available in the existing literature to the best of our knowledge. Particularly, the theoretical conclusions were verified via numerical examples.

Keywords

• new 3d modified chen system
• multi-wing chaotic attractor
• homoclinic and heteroclinic orbit
• lyapunov function