Table 1 The analyzed models of the coevolution between viruses and CRISPR-Cas-carrying hosts

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