A PDE model of clonal plant competition with nonlinear diffusion

► Provide a PDE model adapted to clonal plant competition thanks to cross non linear diffusion. ► We have shown that pattern forming instability cannot occur in general competition systems if the exclusion ability of both species is small even if the diffusions are degenerated. ► Propose a nonlinear reaction-diffusion systems to be a surrogate model for phalanx-guerilla species competition.