Chaotic properties of mechanically and electrically coupled nonlinear dynamical systems. (Chinese. English summary) Zbl 1174.37337

Zhang, Qichang; Tian, Ruilan; Wang, Wei

Acta Phys. Sin. 57, No. 5, 2799-2804 (2008).

Summary: Based on the Silnikov criterion, the chaotic properties of mechanically and electrically coupled nonlinear dynamical systems are discussed. Using Cardano formula and series solution of differential equation, the eigenvalue problem and existence of homoclinic orbit are studied respectively. A rigorous proof of the existence of Silnikov-sense Smale horseshoe chaos is presented and some conditions leading to chaos are obtained. The space trajectory, Lyapunov exponent and Lyapunov dimension are investigated via numerical simulation, which show that chaotic attractors exist in the non-linear dynamical systems.

MSC:

37D45

Strange attractors, chaotic dynamics of systems with hyperbolic behavior

Keywords:

chaotic system; Lyapunov exponent; Silnikov theorem