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

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 M > ad + bs b 1 - s
p =p ( z ) Quasi-chaotic oscillations at all M Damped oscillations at M < Mcr; periodic oscillations at M ≥ Mcr; quasi-chaotic oscillations at M > > Mcr