Competition of two phytoplankton species for light with wavelength (Q896627)

The author studies a model of competition between two phytoplankton species for a single resource-light with wavelength in a well-mixed water column. For the single species the model has the form \[ N'=N\left[\frac{1}{z_m}\int_0^{z_m}g(\gamma(z,N))dz-L\right], \] \[ \gamma(z,N)=\int_0^{\lambda_m}k(\lambda) I(\lambda,z,N)d\lambda, \] \[ I(\lambda,z,N)=I_m(\lambda)e^{-k_0(\lambda)z-k(\lambda)Nz}, ~N(0)>0, \] where \(g(\lambda)\) satisfies the Holling type II functional response. Stability conditions of the positive equilibrium are obtained by the theory of monotone dynamical systems.