School of Mathematics and Statistics’an Jiaotong University Xi’an 710049 P.R.ChinaSchool of Mathematics and Computer Science Xiriyu University Xinyu 338004 P.R.China;
School of Mathematics and Statistics’an Jiaotong University Xi’an 710049 P.R.China;
Predator prey; harvesting; Flip bifurcation; Neimark Sacker bifurcation; chaos.;