In this paper, we investigate the complex dynamics of a spatial plankton-fish system withHolling type III functional responses. We have carried out the analytical study for bothone and two dimensional system in details and found out a condition for diffusiveinstability of a locally stable equilibrium. Furthermore, we present a theoreticalanalysis of processes of pattern formation that involves organism distribution and theirinteraction of spatially distributed population with local diffusion. The results ofnumerical simulations reveal that, on increasing the value of the fish predation rates,the sequences spots → spot-stripe mixtures → stripes → hole-stripe mixtures holes → wavepattern is observed. Our study shows that the spatially extended model system has not onlymore complex dynamic patterns in the space, but also has spiral waves.
