Global asymptotical stability and periodic orbits for competitive Lotka Volterra diffusion system

@inproceedings{He1999GlobalAS,
  title={Global asymptotical stability and periodic orbits for competitive Lotka Volterra diffusion system},
  author={Liu He},
  year={1999}
}
  • Liu He
  • Published 1999
This paper considers a competing system consisting of two species, one of which can diffuse among n-pathes,while the other is confined to one path and can not diffuse.It is proved that if the coefficients satisfy certain inequalities,then the system can have a strictly positive periodic orbit which is globally asymptotically stable.