Abstract
The issue of bifurcation control for a novel fractional-order two-prey and one-predator system with time delay is dealt with in this paper. Firstly, the characteristic equation is investigated by picking time delay as the bifurcation parameter, and some conditions for the appearance of Hopf bifurcation are obtained. It is shown that time delay can give rise to periodic oscillations and each order has an important impact on the occurrence of Hopf bifurcation for the controlled system. Then, it is illustrated that the control result is obviously influenced by the feedback gain. It is also noted that the inception of the bifurcation can be postponed if the feedback gain decreases. Finally, two simulation examples are carried out to verify the chief theoretical results.
Highlights
The dynamic relationship between prey and predator has currently aroused widespread concern from many researchers due to its ubiquitous existence and great importance [1, 2]
The problem of the bifurcation control for an incommensurate fractional-order two-prey and one-predator system with time delay has been investigated at length
The results state clearly that the delay of gestation can give rise to periodic oscillations and the occurrence of Hopf bifurcation can be affected by fractional orders for the controlled system
Summary
The dynamic relationship between prey and predator has currently aroused widespread concern from many researchers due to its ubiquitous existence and great importance [1, 2]. It is well known that fractional-order differential equations relating to memory exist widely in biological systems [16, 17]. Bifurcation control of prey and predator model with time delay is mainly concentrated on state feedback control, which is commonly used in biological control. The problem of bifurcation control for a delayed fractional-order two-prey and one-predator system has not been investigated before. Inspired by the above discussion, we are focused on the topic of a delayed fractional two-prey and one-predator system with disparate orders via a linear state feedback control tool in this paper. The highlights of this paper are the following: (i) a linear time-delayed feedback controller is exploited to complete the bifurcation control in a delayed two-prey and one-predator model and give its biological means.
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
