Abstract
The stability of a kind of cooperative models incorporating harvesting is considered in this paper. By analyzing the characteristic roots of the models and constructing suitable Lyapunov functions, we prove that nonnegative equilibrium points of the models are globally asymptotically stable. Further, the corresponding nonautonomous cooperative models have a unique asymptotically periodic solution, which is uniformly asymptotically stable. An example is given to illustrate the effectiveness of our results.
Highlights
By analyzing the characteristic roots of the models and constructing suitable Lyapunov functions, we prove that nonnegative equilibrium points of the models are globally asymptotically stable
Permanence, stability and periodic solution for LotkaVolterra models had been extensively investigated by many authors
1 m x c 1 m he obtained that harvesting and refuge affected the stability of some coexistence equilibrium and periodic solutions of model (1), where H x was a continuous threshold policy harvesting function
Summary
Permanence, stability and periodic solution for LotkaVolterra models had been extensively investigated by many authors (see [1,2,3,4,5,6,7,8] and the references therein). Jorge Rebaza [1] had discussed the dynamic behaviors of predator-prey model with harvesting and refuge x. He obtained that harvesting and refuge affected the stability of some coexistence equilibrium and periodic solutions of model (1), where H x was a continuous threshold policy harvesting function. Motivated by Jorge’s work, we consider the following cooperative system incorporating harvesting x r1. The parameters r1, r2 , a1, a2 ,b1,b2 , k1, k2 , E, q are all positive constants
Sign-in/Register to view highlights & summary 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.
