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Deformation of limit cycle under perturbations
Affiliation:1. Physics Department, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong SAR, China;2. Key Laboratory of Material Physics, Institute of Solid State Physics, Chinese Academy of Sciences, Hefei, People’s Republic of China;1. Department of Electrical Engineering, National Chi Nan University, 54561, Taiwan;2. Temasek Laboratories, National University of Singapore, 117411, Singapore;1. Indian Institute of Science Education and Research, Computer Science Building, College of Engineering Trivandrum Campus, Trivandrum 695 016 Kerala, India;2. Department of Applied Physics, University of Calcutta, 92, APC Road, Kolkata 700 009, West Bengal, India;3. School of Physical Sciences, National Institute of Science Education and Research, Jatni 752050, India;4. Physics Department, Utkal University, Vani Vihar, Bhuvaneswar 751004, India;1. University of Exeter, Exeter EX4 4QF, UK;2. University of Auckland, Auckland, New Zealand
Abstract:The robustness of limit cycles of nonlinear dynamical systems is investigated by adding a small random velocity field to the famous van der Pol (VDP) equation in its two-dimensional phase plane. Our numerical calculations show that a limit cycle does not change much under a weak random perturbation. Thus it confirms the conjecture that a limit cycle will make only a small deformation under an external perturbation. The idea can be used to understand the ac response of self-sustained oscillations in nonlinear dynamical systems.
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