Lotka-Volterra predator-prey on yearly crime counts — morie_tps_lotka_volterra_police

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)

Arguments

category: TPS category name.
save_fig: Whether to write a yearly time-series PNG.

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

if (FALSE) { # \dontrun{
  rr <- morie_tps_lotka_volterra_police_crime("Assault",
                                                save_fig = FALSE)
  print(rr$summary_lines)
} # }