lotka_volterra_step()

MAYAFLUX_API void MayaFlux::Kinesis::Discrete::lotka_volterra_step	(	std::span< double >	levels,
		std::span< const double >	growth,
		std::span< const double >	interaction,
		double	dt
	)

One explicit step of generalised Lotka-Volterra competition.

Parameters

levels	Nonnegative levels, updated in place
growth	Growth rate of each level
interaction	Row-major N x N matrix; entry (i, j) is how strongly level j suppresses level i, the diagonal being self limitation
dt	Step

Each level changes by dt * a_i * (growth_i - sum_j interaction_ij * a_j), all from the levels at the start of the step, then is held at zero or above. With suppression stronger between entries than within them, the levels take turns instead of settling together. Does nothing when the interaction matrix is smaller than N x N. Uses a per-thread scratch vector, so it allocates only the first time a size is seen.

Definition at line 46 of file Dynamics.cpp.

{
    const size_t n = std::min(levels.size(), growth.size());
    if (n == 0 || interaction.size() < n * n)
        return;
 
    thread_local std::vector<double> next;
    next.assign(n, 0.0);
 
    for (size_t i = 0; i < n; ++i) {
        const double pressure = weighted_sum(levels.first(n), interaction.subspan(i * n, n));
        next[i] = std::max(levels[i] + dt * levels[i] * (growth[i] - pressure), 0.0);
    }
 
    for (size_t i = 0; i < n; ++i)
        levels[i] = next[i];
}

References weighted_sum().

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