Abstract
This paper deals with Gause-type predator-prey models with a non-smooth prey growth rate. Our models have a unique positive equilibrium and are under the influence of an Allee effect. A necessary and sufficient condition is given for the existence of homoclinic orbits whose α \alpha - and ω \omega -limit sets are the positive equilibrium. The argument used here is based on some results of a system of Liénard type. The relation between homoclinic orbits and the Allee effect is clarified. A simple example is included to illustrate the main result. Some global phase portraits are also attached.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
