Abstract
In this paper, we present a predator-prey system with mutual interference and distributed time delay and study its dynamical behavior. Based on the existence and universality of mutual interference among species, it is necessary to further study an impulsive food web system. By using stability theory, slight perturbation technique, and comparison theorem, we obtain some theoretical results of the system, such as boundedness and permanence. Moreover, numerical experiments are used to verify the theoretical results and to explore the dynamical behavior of the system, which exhibits rich dynamical behavior such as chaotic oscillation, periodic oscillation, symmetry-breaking bifurcations, chaotic crises, and period bifurcation. Finally, we give some practical guidelines for biological systems based on the theoretical results and numerical experiments of the system.
Highlights
In the past few decades, food web or food chain predatorprey system has been widely studied by many scholars
Suppose z∗(t) is a positive periodic solution of system (13), for each solution z(t) with z(0+) ≥ 0, it follows that |z(t) − z∗(t)| ⟶ 0 as t ⟶ ∞
When T 22.61, a typical chaotic oscillation appears (see Figure 5(c)); after this situation, chaos appears such as Figure 6(d) (T 22.8). at is to say, when T is less than 17.85, the harvesting and release of the system is frequent; when 17.85 < T < 20.66, period bifurcation appears; if 20.66 < T < 23, the dynamical properties of the system (8) become very complex; that is, the development of the system is unpredictable. All these results indicate that impulsive period T has a serious effect on the dynamic behavior of the system
Summary
In the past few decades, food web or food chain predatorprey system has been widely studied by many scholars. Some impulsive predator-prey models with distributed time delays are investigated; for example, these papers [23,24,25] showed some theoretical results and guiding significance of several impulsive systems with distributed time delays. Guo and Chen [29] explored a predator-prey model with mutual interference as follows: k1(t)x(t) ym(t), a + bx(t) + cy(t). Sahoo and Poria [34] applied a technique of controlling chaotic predator-prey population dynamics by supplying additional food to the top predator, which study is aimed to introduce a new nonchemical chaos control mechanism in a predator-prey system with the applications in fishery management and biological conservation of prey-predator species. Our main purpose is to explore the effect of mutual interference in an impulsive food web with distributed time delays.
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.
