Turing instability and wave patterns for a symmetric discrete competitive Lotka-Volterra system

Abstract

In this paper, Turing instability of a symmetric discrete competitive Lotka-Volterra system is considered. To this end, conditions for producing Turing instability of a general discrete system is attained and this conclusion is applied to the discrete competition Lotka-Volterra system. Then a series of numerical simulations of the discrete model are performed with different parameters. Results show that the discrete competitive Lotka-Volterra system can generate a large variety of wave patterns in the Turing instability region. Particularly, the diffusion coefficients can be equivalent, that is, there is neither activator nor inhibitor. Similar results can not be obtained for the corresponding continuous models. On the other hand, the number of the eigenvalues is illuminated by calculation and the unstable spaces can be clearly expressed. Thus, the Turing mechanism is also explained.