2018/12/25 by Jyoti Prasad Deka, Deka, Jyoti Prasad, A. Govindarajan +5
Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Mechanical and Optical Resonators #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.1812.10126
openalex publication_date 2018/12/25 · openalex created_date 2022/08/01 · openalex updated_date 2026/07/28
We propose a generalized parity-time (\PT) -symmetric Li 'enard\noscillator with two different orders of nonlinear position-dependent\ndissipation. We study the stability of the stationary states by using the\neigenvalues of Jacobian and evaluate the stability threshold thereafter. In the\nfirst order nonlinear damping model, we discover that the temporal evolution of\nboth gain and lossy oscillators attains a complete convergence towards the\nstable stationary state leading to the emergence of oscillation and amplitude\ndeaths. Also, the system displays a remarkable manifestation of transient chaos\nin the lossy oscillator while the gain counterpart exhibits blow-up dynamics\nfor certain choice of initial conditions and control parameters. Employing an\nexternal driving force on the loss oscillator, we find that the blow-up\ndynamics can be controlled and a pure aperiodic state is achievable. On the\nother hand, the second order nonlinear damping model yields a completely\ndifferent dynamics on contrary to the first order where the former reveals a\nconventional quasi-periodic route to chaos upon decreasing the natural\nfrequency of both gain and loss oscillators. An electronic circuit scheme for\nthe experimental realization of the proposed system has also been put forward.\n