An application of topological degree to the periodic competing species problem

Carlos Alvarez, Alan C. Lazer
1986 The Journal of the Australian Mathematical Society Series B Applied Mathematics  
We consider the Volterra-Lotka equations for two competing species in which the right-hand sides are periodic in time. Using topological degree, we show that conditions recently given by K. Gopalsamy, which imply the existence of a periodic solution with positive components, also imply the uniqueness and asymptotic stability of the solution. We also give optimal upper and lower bounds for the components of the solution.
doi:10.1017/s0334270000005300 fatcat:jwsw6zszvjc4xggtrmmfpmppfq