Perturbative dynamics of stationary states in nonlinear parity-time symmetric coupler

•Stability of stationary points in a nonlinear parity-time symmetric coupler is investigated.•Instabilities in initial conditions can lead to aperiodic oscillations.•The existence of a stable attractor under the influence of fluctuating gain/loss coefficient is observed.•Presence of a toroidal chaot...

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Bibliographic Details
Published in:Communications in nonlinear science & numerical simulation 2018-04, Vol.57, p.26-33
Main Authors: Deka, Jyoti Prasad, Sarma, Amarendra K.
Format: Article
Language:English
Subjects:
Attractor
Coupler
Couplers
Initial conditions
Nonlinear systems
Parity
Parity-time symmetry
Phase transitions
Quantum physics
Schrodinger equation
Stability analysis
Variations
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Summary:•Stability of stationary points in a nonlinear parity-time symmetric coupler is investigated.•Instabilities in initial conditions can lead to aperiodic oscillations.•The existence of a stable attractor under the influence of fluctuating gain/loss coefficient is observed.•Presence of a toroidal chaotic attractor is reported. We investigate the nonlinear parity-time (PT) symmetric coupler from a dynamical perspective. As opposed to linear PT-coupler where the PT threshold dictates the evolutionary characteristics of optical power in the two waveguides, in a nonlinear coupler, the PT threshold governs the existence of stationary points. We have found that the stability of the ground state undergoes a phase transition when the gain/loss coefficient is increased from zero to beyond the PT threshold. Moreover, we found that instabilities in initial conditions can lead to aperiodic oscillations as well as exponential growth and decay of optical power. At the PT threshold, we observed the existence of a stable attractor under the influence of fluctuating gain/loss coefficient. Phase plane analysis has shown us the presence of a toroidal chaotic attractor. The chaotic dynamics can be controlled by a judicious choice of the waveguide parameters.
ISSN:1007-5704
1878-7274
DOI:10.1016/j.cnsns.2017.09.015