College of Mathematics and Information Science Anshan Normal University Anshan 114007 Liaoning R.China;
Department of Mathematics Liaoning Normal University Dalian 116029 Liaoning P.R.China;
College of Mathematics and Information Science Anshan Normal University Anshan 114007 Liaoning R.China;
College of Mathematics and Information Science Anshan Normal University Anshan 114007 Liaoning R.China;
Pulse pollution; invasion fitness function; evolutionary singulary strategy; evolutionary branching; coevolution;