From: Pseudo-chaotic oscillations in CRISPR-virus coevolution predicted by bifurcation analysis
Two-component model | ||
---|---|---|
Malthusian | Logistic | |
p = const | Center M > p/(1-p) | Damped oscillations M > p/(1-p) |
p = p ( z ) | No stable equilibrium z > 0 | Damped oscillations M > M* (finite or infinite basin of attraction) |
Three-component model | ||
Malthusian | Logistic | |
p = const | Damped oscillations M > p/(1-p) or s/(1-s) < M < p/(1-p) and l > l(e) | Stable equilibrium for $\mathrm{M}>\frac{\mathrm{\text{ad}}+\mathrm{\text{bs}}}{\mathrm{b}\left(1-\mathrm{s}\right)}$ |
p = p ( z ) | Quasi-chaotic oscillations at all M | Damped oscillations at M < M^{cr}; periodic oscillations at M ≥ M^{cr}; quasi-chaotic oscillations at M > > M^{cr} |