Dynamics of a lattice gas system of three species

摘要: Abstract This paper considers a mutualism system of three species in which each provides resource for the next one one-directional loop, while there exists spatial competition among them. The is characterized by lattice gas model and cases obligate mutualisms, obligate–facultative mutualisms facultative are considered. Using dynamical systems theory, it shown that (i) can lead to coexistence species; (ii) A weak or an extremely strong will result extinction species, even superior be driven into its over-strong on one; (iii) Initial population density plays role species. It also when mutualism, survive providing more benefit one, inferior not if strengthen Moreover, Hopf bifurcation, saddle-node bifurcation heteroclinic cycles system. Projection method extended exhibit bistability three-dimensional model: occurs, stable manifold point divides int R + 3 two basins attraction equilibria. Furthermore, Lyapunov applied unstability cycles. Numerical simulations confirm extend our results.