Fig. 1: Numerical results of lattice size-dependent non-Hermitian topological synchronization.

a The top chart illustrates a schematic of a two-dimensional lattice model featuring onsite nonlinear oscillators. The intra-cell and inter-cell couplings correspond to the site couplings within the same and different units. The bottom chart illustrates the creation of non-Hermitian topological synchronization induced by the interplay among non-Hermitian physics, topological states, and nonlinearity. b1, b2 Numerical results of time-domain dynamics of \({S}_{e}(t)={{\mathrm{Re}}}\{{\sum }_{i\in {N}_{e}}{{\mathrm{Z}}}_{{\mathrm{i}}}\left({{\mathrm{t}}}\right)/{{\mathrm{N}}}_{{\mathrm{e}}}\}\) and \({S}_{b}(t)={{\mathrm{Re}}}\{{\sum }_{i\in {N}_{b}}{{\mathrm{Z}}}_{{\mathrm{i}}}\left({{\mathrm{t}}}\right)/{{\mathrm{N}}}_{{\mathrm{b}}}\}\) for the system with \({N}_{x}={N}_{y}=5\). b3 Numerical results of frequency spectra obtained from the discrete Fourier transform on \({S}_{e}(t)\) and \({S}_{b}(t)\) in b1, b2. Numerical results of \({S}_{e}\left(t\right),\,{S}_{b}(t)\) and the corresponding frequency spectra are shown in c1–c3 for \({N}_{x}={N}_{y}=8\) and (d1–d3) for \({N}_{x}={N}_{y}=21\).