Dynamical Behaviors Of Several Systems With Harvesting Terms

This paper consists of three parts:Firstly, the existence of multiple periodic solutions for a three species predatorprey Lotka-Volterra system with harvesting is proposed, by using of the coincidencedegree, the sufficient conditions of the existence of eight periodic solutions areobtained. Further, the numerical simulations confirmed the theoretical results. Basingon the results of three species Lotka-Volterra system, n-species system withharvesting, delay and functional response is investigated, then, the sufficientconditions of the existence to2nperiodic solutions of n-species system are obtainedby coincidence degree.Secondly, the existence of multiple positive periodic solutions to a three speciescompetition-predator system with harvesting, delay and dispersion are studied,making use of the coincidence degree, we obtain the sufficient conditions of theexistence for eight periodic solutions. Further, we give a concrete example to confirmthat harvesting terms always play an important role in the dynamical behavior ofpopulation.Finally, we study a one-prey multi-predators ecosystems with B-D functionalresponse and impulsive control, by using of the Floquet theory and the comparisontheorem of impulsive differential equation, sufficient conditions to the stability ofpositive periodic solution that ensuring the prey-extinction and predator-permanenceare obtained, further, sufficient conditions for the permanence of the system areobtained.