Canonical Short-D'Orsogna-Brantingham Turing-pattern demo

Reproduces the localised hot-spot lattice from Short, D'Orsogna & Brantingham (2008) Fig. 4 / D'Orsogna & Perc (2015) Fig. 5 on a clean periodic grid, seeded by a homogeneous steady state plus small Gaussian noise. The parameters chosen here place the system in the Turing-instability regime so the homogeneous solution is unstable and the system self-organises into a near-hexagonal lattice of localised spikes.

Usage

morie_tps_sdb_turing_demo(
  eta = 0.2,
  omega = 0.033,
  theta = 0.56,
  D = 30,
  gamma = 0.019,
  n_steps = 6000L,
  dt = 0.005,
  n = 80L,
  save_fig = TRUE
)

Arguments

eta, omega, theta, D, gamma

PDE coefficients.

n_steps

Integration steps.

dt

Step size.

n

Grid side length.

save_fig

Whether to write a 1x3 snapshot panel PNG.

Value

A morie_rich_result with the steady-state spike count, mean fields, and the integration parameters.

References

Short MB, D'Orsogna MR, Brantingham PJ et al. (2008). M3AS 18(supp01): 1249-1267.

Examples

if (FALSE) { # \dontrun{
  rr <- morie_tps_sdb_turing_demo(n = 32L, n_steps = 300L,
                                    save_fig = FALSE)
  print(rr$summary_lines$SteadySpikes)
} # }