Browsing by Author "Aman Kumar Singh"

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Effects of nonlinear capacitance in feedback LC-tank on chaotic Colpitts oscillator
(Institute of Physics Publishing, 2020) Saumitra Mishra; Aman Kumar Singh; R.D.S. Yadava
This manuscript presents modifications of the standard Colpitts circuit by replacing one of the capacitors in C 1 - C 2 potential divider by a pair of back-to-back connected diode varactor. This introduces a nonlinearity of diode varactor type in the feedback signal generation itself. The dynamic capacitance of the varactor pair varies nonlinearly with the output voltage. The proposed modification facilitates generation of enriched frequency components with enhanced power. Both C 1 and C 2 were alternately replaced by the diode varactor and results were compared with the standard oscillator with fixed-value capacitors. The analysis is based on basic numerical tools such as Lyapunov exponents, bifurcation diagram, phase trajectories and power spectra. © 2020 IOP Publishing Ltd.
QES solutions of a two-dimensional system with quadratic nonlinearities
(Springer Science and Business Media Deutschland GmbH, 2020) Bhabani Prasad Mandal; Brijesh Kumar Mourya; Aman Kumar Singh
We consider a one-parameter family of a PT symmetric two-dimensional system with quadratic nonlinearities. Such systems are shown to perform periodic oscillations due to existing centers. We describe this system by constructing a non-Hermitian Hamiltonian of a particle with position-dependent mass. We further construct a canonical transformation which maps this position-dependent mass system to a QES system. First few QES levels are calculated explicitly by using Bender–Dunne polynomial method. © 2020, Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature.
Synchronization and amplitude death in a pair of Van der Pol oscillators under conjugate coupling
(Institute of Physics Publishing, 2019) Aman Kumar Singh; R.D.S. Yadava
This work presents an analysis of synchronization and amplitude death (oscillation decay) phenomena in a pair of coupled Van der Pol oscillators under two types of conjugate couplings. The coupling is through diffusive flow of the conjugate or dissimilar variables and referred to as type 1 and type 2 coupling respectively. The analytical conditions for in-phase and out-of-phase synchronizations and amplitude death are determined. It is found that the amplitude death occurs only with type 2 coupling over a region of coupling strength. In this region, with decaying amplitude the oscillators approach a stationary state of negligible amplitude in anti-phase fashion. Beyond this range, on lower side the stable in-phase synchronization occurs if the frequencies of both the oscillators are equal, and on higher side uncontrolled amplitude growth occur. The type 1 coupling produces stable in-phase synchronization for positive coupling strength values and stable anti-phase synchronization for negative values under the condition that the coupling strength must be greater than or equal to the frequency detuning. In coupled systems the synchronization conditions are achieved maintaining the linear phase characteristics similar to the uncoupled oscillators. This study may be of interest in modeling the behavior of coupled biological and electrical oscillators. © 2019 IOP Publishing Ltd.
Transient motion and chaotic dynamics in a pair of van der Pol oscillators
(Springer Verlag, 2019) Aman Kumar Singh; R.D.S. Yadava
The transient chaos and the stable chaotic dynamics of coupled autonomous van der Pol (VdP) oscillators with cubic term are investigated. Transient chaos is a common phenomenon in externally driven van der Pol oscillators. Nevertheless, in coupled autonomous VdP oscillators the occurrence of transient chaos, even stable chaos, is a rare scenario. To the best of our knowledge, transient chaos has not often been observed in coupled autonomous van der Pol systems. We demonstrate that the nonlinear restoring forces in a pair of van der Pol oscillators can induce a transient chaotic route to deterministic chaos. The symmetric coupling has been considered and provided by perturbing the amplitude of one oscillator by a fraction another oscillator's amplitude. The coupled systems undergo a crisis when the coupling parameter passes through a certain threshold. The crisis occurs when the chaotic attractor behaves as a chaotic repeller for a transient time and transient chaos emerges. After transient motion, the system's dynamics is attracted either to a periodic motion or stationary state. The Lyapunov spectrum, bifurcation diagram, phase space trajectories and Poincaré section were used to study the chaotic motion. The effects of nonlinear restoring force have been investigated through bifurcation diagram. © 2019, Società Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature.