The Influence Of Mutations On Replication Dynamics

By using mathematics method, Replication dynamics describe changes in theproportion of each sub-population of the population, which tracks more and more mathemati-cians and biologists’attention. Replication, selection and mutation are the three fundamentalprinciples of the evolutionary dynamics. This paper aims at introducing a mutation basedon M.Bomze’s forty-seven kinds of classification of3D replication dynamics, examining theexistence and numbers of system’s limit cycle and the dynamic behavior of the system whenmutation is introduced under certain conditions.This paper consists of six chapters:The first chapter is the introduction.The second chapter describes the basic theory and Hopf bifurcation of planar systems.The third chapter gives a derivation of replication dynamics as well as Bomze’s forty-sevenclassifications.The fourth chapter studies the impact of mutations on replication dynamics under certainconditions.The fifth chapter makes limit cycle for some system which is from forty-seven classifica-tions after introducing mutation under certain conditions.The sixth chapter summarizes this paper and does some outlook for further work.Appendix is a the Maple procedure to be used..