Multistability and Jump in the Harmonically Excited SD Oscillator

Fractal and Fractional

article

Zhenhua Wang¹  Huilin Shang¹ 

[1] School of Mechanical Engineering, Shanghai Institute of Technology

关键词: SD oscillator;    multistability;    jump;    hidden attractor;    basin of attraction;    fractal;   

DOI  :  10.3390/fractalfract7040314

学科分类：社会科学、人文和艺术（综合）

来源: mdpi

【 摘 要 】

Coexisting attractors and the consequent jump in a harmonically excited smooth and discontinuous (SD) oscillator with double potential wells are studied in detail herein. The intra-well periodic solutions in the vicinity of the nontrivial equilibria and the inter-well periodic solutions are generated theoretically. Then, their stability and conditions for local bifurcation are discussed. Furthermore, the point mapping method is utilized to depict the fractal basins of attraction of the attractors intuitively. Complex hidden attractors, such as period-3 responses and chaos, are found. It follows that jumps among multiple attractors can be easily triggered by an increase in the excitation level or a small disturbance of the initial condition. The results offer an opportunity for a more comprehensive understanding and better utilization of the multistability characteristics of the SD oscillator.

【 授权许可】

CC BY