Wang, Lesheng2018-04-052018-04-052017https://hdl.handle.net/11299/195236University Honors Capstone Project Paper and Poster, University of Minnesota Duluth, 2017. Department of Mathematics and Statistics. Faculty Advisor: Dr. Bruce Peckham.Some of the dynamics of the family x→x^2+c+β/x^d are described. Different behaviors occur as the parameter β and c are varied. These transitions are called bifurcations. This singular perturbed quadratic family is treated both as a real system. This paper is based on the various trials done in the Mathematica 10. The main focus of this paper is done for the parameter β and c. Specifi cally, the summary is done to present the general behaviors of the real case. Meanwhile, this paper creates some general behaviors of the system with different parameter d. The dynamics of one dimensional quadratic maps is present.enBifurcationsSingular perturbed quadratic familyMathematica 10Parameter ?Parameter cDifferential equationsDiscrete dynamical systemsUniversity of Minnesota DuluthUniversity HonorsScholarly Text or Essay