Abstract
In nature, a biological invasion is a common phenomenon that often threatens the existence of local species. Getting rid of the invasive species is hard to achieve after its survival and reproduction. At present, killing some invasive ones and putting artificial local species are usual methods to prevent local species from extinction. An ODE model is constructed to simulate the invasive procedure, and the protection policy is depicted as a series of impulses depending on the state of the variables. Both the ODEs and the impulses form a state feedback impulsive model which describes the invasion and protection together. The existence of homoclinic cycle and bifurcation of order-1 periodic solution of the impulsive model are discussed, and the orbitally asymptotical stability of the order-1 periodic solution is certificated with a novel method. Finally, the numerical simulation result is listed to confirm the theoretical work.
Highlights
Biological invasion is the introduction and establishment of a species beyond its natural range where it may proliferate and spread dramatically [1]
When local community members are challenged by biological invasions, they may face novel antagonists such as predators or competitors, or they may benefit from new prey, new and underutilized host plants, or even new mutualists [6]
Since biological invasions contribute a lot to rapid environmental change [8], biodiversity loss, degradation of ecosystem structure, impairment of ecosystem services [9], and significant impacts on both natural and agricultural ecosystems [10], ecological invasion and subsequent influence are receiving increasing attention from scientists and governors
Summary
Biological invasion is the introduction and establishment of a species beyond its natural range where it may proliferate and spread dramatically [1]. Since biological invasions contribute a lot to rapid environmental change [8], biodiversity loss, degradation of ecosystem structure, impairment of ecosystem services [9], and significant impacts on both natural and agricultural ecosystems [10], ecological invasion and subsequent influence are receiving increasing attention from scientists and governors. Inspired by the new results in state feedback impulsive model [16,17,18,19,20,21,22,23,24,25,26], and classical work in limit cycle [26] the authors propose a state feedback impulsive model, which is more suitable than the ODE model, to describe the procedure of ecological invasion and artificial control.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
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 call
