Dissipative structures in a parametrically driven dissipative lattice: chimera, localized disorder, continuous-wave, and staggered state

TL;DR

This paper explores complex behaviors like chimera states, localized disorder, and phase transitions in a parametrically driven dissipative lattice modeled by a nonlinear Schrödinger equation, revealing stable localized states and dynamical phase changes.

Contribution

It introduces a detailed analysis of chimera and localized states in a driven dissipative lattice, combining numerical simulations with analytical insights to map stability regions.

Findings

Identification of stable localized states in parameter space

Observation of a phase transition from disorder to chaos

Quantification of chimera dynamics via Lyapunov exponents

Abstract

Discrete dissipative coupled systems exhibit complex behavior such as chaos, spatiotemporal intermittence, chimera among others. We construct and investigate chimera states, in the form of confined stationary and dynamical states in a chain of parametrically driven sites with onsite damping and cubic nonlinearity. The system is modeled by the respective discrete parametrically driven damped nonlinear Schrodinger equation. Chimeras feature quasi-periodic or chaotic dynamic in the filled area, quantified by time dependence of the total norm (along with its power spectrum), and by the largest Lyapunov exponent. Systematic numerical simulations, in combination with some analytical results, reveal regions in the parameter space populated by stable localized states of different types. A phase transition from the stationary disorder states to spatially confined dynamical chaotic one is identified. Essential parameters of the system are the strength and detuning of the forcing, as well as the lattice's coupling constant.