Eur. Phys. J. Special Topics 229, 1245-1255 (2020)
https://doi.org/10.1140/epjst/e2020-900167-1

Regular Article

Time varying feedback control on multi-stability in hidden attractor

¹ Department of Physics, Central University of Rajasthan, Ajmer 305 817, India
² Department of Physics & Astrophysics, University of Delhi, Delhi 110 007, India
³ Saint-Petersburg State University, St. Petersburg, Russia
⁴ Department of Mathematical Information Technology, University of Jyväskylä, Jyväskylä, Finland

^a e-mail: shrimali@curaj.ac.in

Received: 13 August 2019
Received in final form: 16 October 2019
Published online: 26 March 2020

Abstract

We study a on-off feedback method to control the dynamics of a radio physical oscillator having hidden coexisting attractors. The proposed time-varying on-off feedback effectively controls the multi-stability which acts in an on-off manner. We show that for suitable values of feedback strength, feedback active time ratio and time period, the coexisting chaotic and periodic dynamics of the system go to a mono-stable periodic state followed by a stable steady state. This transition from multiple attractors to a single attractor is confirmed by calculating bifurcation diagram, Lyapunov exponent and the basin size as a measure. We also illustrate the generation of chaotic attractor in the system using this scheme.