Lotka-Volterra predator-prey on yearly crime counts

Treats yearly category counts as the prey \(x(t)\) and a 3-year rolling mean as a placeholder predator \(y(t)\) (TPS does not yet expose a public mass-stop / use-of-force time series). Under the classical Lotka-Volterra system, $$\dot x = \alpha x - \beta x y, \quad \dot y = \delta x y - \gamma y,$$ the small-amplitude oscillation around the equilibrium has period \(T = 2 \pi / \sqrt{\alpha \gamma}\). Growth rate \(\alpha\) is estimated from log-differences of x; \(\gamma\) symmetrically from y; the interaction rates \(\beta, \delta\) follow by the equilibrium relations.

Usage

morie_tps_lotka_volterra_police_crime(
  category = "Assault",
  save_fig = TRUE,
  fig_dir = NULL
)

Arguments

category

TPS category name.

save_fig

Whether to write a yearly time-series PNG.

fig_dir

Directory to write the PNG into; NULL (the default) skips writing and says so in the result.

Value

A morie_rich_result with the four LV parameters, the linearised cycle period, the year range, and a qualitative interpretation.

References

D'Orsogna MR, Perc M (2015). Statistical physics of crime: A review. Physics of Life Reviews 12: sec. 3.4.

Examples

# \donttest{
  rr <- morie_tps_lotka_volterra_police_crime("Assault",
                                                save_fig = FALSE)
#> morie_tps: no local TPS cache for 'Assault'; using the bundled sample from rmoriedata. Fetch the full export with morie_tps_fetch_category().
  print(rr$summary_lines)
#> $Method
#> [1] "LV predator-prey on yearly counts (D&P 2015 sec. 3.4)"
#> 
#> $Years
#> [1] "2014-2026"
#> 
#> $alpha
#> [1] 0.064
#> 
#> $beta
#> [1] 0.00082
#> 
#> $gamma
#> [1] 0.039
#> 
#> $delta
#> [1] 5e-04
#> 
#> $cycle_yr
#> [1] 126.3
#> 
#> $Figure
#> [1] "(skipped)"
#> 
# }