Existence of positive periodic solutions of a neutral delay Lotka-Volterra system with impulses

• Authors: Hai-Feng Huo
• Venue: Computers & Mathematics with Applications
• Year: 2004

Sufficient conditions are obtained for the existence of periodic positive solutions of a class of neutral impulsive delay Lotka-Volterra systems N"i^'(t)=N"i(t)[@a"i(t)-@?j=1n@b"i"j(t)N"j(t-@t"i"j(t))-@?j=1nc"i"j(t)N"j^'(t-@c"i"j(t))],N"i(t"k^+)-N"i(t"k)=b"i"kN"i(t"k),i=1,2,...,n,k=1,2,..., by using some techniques of Mawhin coincidence degree theory. My results generalize some known results. It is shown that under the appropriate linear periodic impulsive perturbations, the neutral impulsive delay Lotka-Volterra system preserves the original periodicity of the neutral nonimpulsive delay Lotka-Volterra system.