Is this delay-coupled oscillator formulation for a 3D phononic lattice physically correct?

I'm modeling a 3D lattice of piezoelectric resonators,
where each node is coupled to its nearest neighbors
with a propagation time delay (representing finite
wave speed between nodes), and driven by thermal noise.

The governing equation for node $i$ is:

$\frac{d^2u_i}{dt^2} + \gamma\frac{du_i}{dt} + \omega_i^2 u_i = \sum_{j} K_{ij} \cdot u_j(t - \tau_{ij}) + F_{th}(t)$

Where:

• $u_i$ = displacement of resonator $i$

• $\gamma$ = damping coefficient

• $\omega_i$ = natural frequency of resonator $i$

• $K_{ij}$ = coupling strength to neighbor $j$

• $\tau_{ij}$ = propagation delay to neighbor $j$ (based on distance and wave speed in the medium)

• $F_{th}(t)$ = thermal (Langevin) noise force

Questions:

1. Is this a correct formulation of a delay-coupled oscillator network, or am I missing terms (e.g. second-order delay effects, retardation corrections)?

Context: I'm investigating whether constructive/destructive interference patterns in such a lattice could represent computational states (an analog optimization process). Just want to confirm the underlying oscillator model is physically sound before going further.