Nonlinear resonance in Duffing oscillator with fixed and integrative time-delayed feedbacks

Pramana

V Ravichandran¹  S Rajasekar²  V Chinnathambi1¹ 

[1] Department of Physics, Sri K.G.S. Arts College, Srivaikuntam 628 619, India$$;School of Physics, Bharathidasan University, Thiruchirapalli 620 024, India$$

关键词: Duffing oscillator;    nonlinear resonance;    time-delayed feedback;    hysteresis.;   

DOI  :  

学科分类：物理（综合）

来源: Indian Academy of Sciences

【 摘 要 】

We study the nonlinear resonance, one of the fundamental phenomena in nonlinear oscillators, in a damped and periodically-driven Duffing oscillator with two types of time-delayed feedbacks, namely, fixed and integrative. Particularly, we analyse the effect of the time-delay parameter 𝛼 and the strength 𝛾 of the time-delayed feedback. Applying the perturbation theory we obtain a nonlinear equation for the amplitude of the periodic response of the system. For a range of values of 𝛾 and 𝛼, the response amplitude is found to be higher than that of the system in the absence of delayed feedback. The response amplitude is periodic on the parameter 𝛼 with period 2𝜋 /𝜔 where 𝜔 is the angular frequency of the external periodic force. We show the occurrence of multiple branches of the response amplitude curve with and without hysteresis.

【 授权许可】

Unknown