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

Abstract Discrete dissipative coupled systems exhibit complex behavior such as chaos, spatiotemporal intermittence, chimeras 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 dynamics 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 disordered 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.