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

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 dynamical states a chain parametrically driven sites with onsite damping cubic nonlinearity. The system is modeled by respective discrete damped nonlinear Schrödinger equation. Chimeras feature quasi-periodic or chaotic dynamics filled area, quantified time dependence total norm (along its power spectrum), largest Lyapunov exponent. Systematic numerical simulations, combination some analytical results, reveal regions parameter space populated stable localized different types. A phase transition from disordered to spatially one identified. Essential parameters are strength detuning forcing, well lattice’s coupling constant.