https://doi.org/10.1140/epjb/s10051-025-00926-1
Regular Article - Statistical and Nonlinear Physics
Asymmetric coupling and nonlinear resonance in coupled anharmonic oscillators
1
Department of Physics, Anna University, 600025, Chennai, Tamil Nadu, India
2
Centre for Nonlinear and Complex Networks, SRM Institute of Science and Technology, 600089, Ramapuram, Chennai, India
3
Centre for Nonlinear and Complex Networks, SRM TRP Engineering College, 621 105, Tiruchirapalli, Tamil Nadu, India
4
Center for Research, SRM Institute of Science and Technology, 600089, Ramapuram, Chennai, India
5
Center for Research, Easwari Engineering College, 600089, Ramapuram, Chennai, India
6
Center for Cognitive Science, Trichy SRM Medical College Hospital and Research Center, Trichy, India
Received:
25
February
2025
Accepted:
10
April
2025
Published online:
18
July
2025
Bidirectional coupling with unequal strengths in a nonlinear system leads to complex and diverse dynamics. In this work, we investigate the emergence of resonance in a system of bidirectionally coupled Duffing oscillators with different coupling strengths in each direction, treating these asymmetric coupling strengths as control parameters. Using a theoretical approach, we derive frequency response relations for a system of two Duffing oscillators coupled bidirectionally with distinct coupling strengths. Notably, both oscillators exhibit a resonance peak in the response amplitude curve under a weak periodic input signal. The validity of our theoretical expressions is confirmed through numerical simulations. Furthermore, we examine the effects of asymmetric interactions between the two oscillators. Our results show that the resonance behavior of each oscillator emerges with a monotonic increase in either of the coupling strengths. Additionally, we analyze how system parameters, along with the two coupling strengths, influence the response amplitude. Finally, we find that as the coupling strengths vary, the system exhibits hysteresis phenomena in both oscillators.
Copyright comment Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
