Dissipative structures in a parametrically driven dissipative lattice: chimera, localized disorder, continuous-wave, and staggered state
arXiv:2103.07748 · doi:10.1016/j.chaos.2021.110880
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.
arXiv commentTo be published in Chaos, Solitons and Fractals
References in corpus (35)
- Chimera States for Coupled Oscillators
- Chimera states: Coexistence of coherence and incoherence in networks of coupled oscillators
- Coexistence of Coherence and Incoherence in Nonlocally Coupled Phase Oscillators
- Loss of coherence in dynamical networks: spatial chaos and chimera states
- Nonlinear Waves in Bose-Einstein Condensates: Physical Relevance and Mathematical Techniques
- Chimera states: The Existence Criteria Revisited
- Chimera states in heterogeneous networks
- Localized States in Discrete Nonlinear Schrödinger Equations
- A classification scheme for chimera states
- Nonlinear Tight-Binding Approximation for Bose-Einstein Condensates in a Lattice
- Collective Excitations of a One-Dimensional Quantum Droplet
- Spontaneous Symmetry Breaking in Photonic Lattices: Theory and Experiment
- Multistable Solitons in the Cubic-Quintic Discrete Nonlinear Schrödinger Equation
- Impurity-induced stabilization of solitons in arrays of parametrically driven nonlinear oscillators
- Intrinsic localized modes in parametrically-driven arrays of nonlinear resonators
- Chimera in a neuronal network model of the cat brain
- Higher-order vortex solitons, multipoles, and supervortices on a square optical lattice
- Two and three-dimensional oscillons in nonlinear Faraday resonance
- Multistable Solitons in Higher-Dimensional Cubic-Quintic Nonlinear Schroedinger Lattices
- Localized patterns and hole solutions in one-dimension extended sytem
- Families of spatial solitons in a two-channel waveguide with the cubic-quintic nonlinearity
- The changing notion of chimera states, a critical review
- Atomic Josephson vortex
- Dynamics and Pattern Formation in Large Systems of Spatially-Coupled Oscillators with Finite Response Times
- Soliton complexity in the damped-driven nonlinear Schrödinger equation: stationary, periodic, quasiperiodic complexes
- Discrete solitons in electromechanical resonators
- Quantifying Spatiotemporal Chaos in Rayleigh-Bénard Convection
- Standing lattice solitons in the discrete NLS equation with saturation
- Probing quasi-integrability of the Gross-Pitaevskii equation in a harmonic-oscillator potential
- Soliton-radiation coupling in the parametrically driven, damped nonlinear Schrödinger equation
- Variational approximations for travelling solitons in a discrete nonlinear Schrödinger equation
- Multistable Pulse-like Solutions in a Parametrically Driven Ginzburg-Landau Equation
- Stability of Discrete Solitons in the Presence of Parametric Driving
- Localized Faraday patterns under heterogeneous parametric excitation
- Justification of the discrete nonlinear Schrödinger equation from a parametrically driven damped nonlinear Klein-Gordon equation and numerical comparisons