In this paper, a Leslie predator–prey system with ratio-dependent and state impulsive feedback control is investigated by applying the geometry theory of differential equation. When the economic threshold level is under the positive equilibrium, the existence, uniqueness and orbital asymptotical stability of order-1 periodic solution for the system can be obtained. When the economic threshold level is above the positive equilibrium, and the positive equilibrium is a focus point, sufficient conditions of the existence, uniqueness and orbital asymptotical stability of order-1 periodic solution for the system are also acquired. Furthermore, when the positive equilibrium is an unstable focus point, the existence of order-1 periodic solution of the impulsive system can be obtained within limit cycle of the continuous system. The mathematical results can be verified by numerical simulations.
Nonlinear Dynamics – Springer Journals
Published: Jul 3, 2017
It’s your single place to instantly
discover and read the research
that matters to you.
Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.
All for just $49/month
Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly
Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.
Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.
Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.
All the latest content is available, no embargo periods.
“Hi guys, I cannot tell you how much I love this resource. Incredible. I really believe you've hit the nail on the head with this site in regards to solving the research-purchase issue.”Daniel C.
“Whoa! It’s like Spotify but for academic articles.”@Phil_Robichaud
“I must say, @deepdyve is a fabulous solution to the independent researcher's problem of #access to #information.”@deepthiw
“My last article couldn't be possible without the platform @deepdyve that makes journal papers cheaper.”@JoseServera