A novel periodically forced Filippov Holling II prey-predator model by applying threshold policy control (TPC) and integrated pest management (IPM) strategies is proposed, and the periodic forcing is described as a Fourier series with different forcing terms. Our work is aim to address how periodic forcing affects dynamic behaviors of the proposed system and to reasonably realize pest control. Based on the above considerations, the relations between sliding region and sliding periodic solution of the Filippov system are analyzed. Then, the existence conditions of sliding periodic solution and its global stability are addressed. Further, numerical investigations related to bifurcation analysis of crucial parameters including the amplitude of forcing terms, economic threshold (ET ) and the frequency of forcing terms are discussed. More importantly, the real biological implications are also addressed. Our results show that the globally stable sliding periodic solution could always lie in the sliding region, which indicates that the density of pest populations cannot reach and exceed the economic injury level (EIL), namely, the pest control is successful. Moreover, the results reveal that various complex dynamics of the Filippov system contains multiple attractors coexistence, switching transients and chaotic phenomena. In addition, the attraction basins of the coexisting attractors reveal that these two populations could be monitored and tracked carefully for the successful pest control, which depends on their initial density. INDEX TERMSHolling II prey-predator system, periodic forces, pest control, bifurcation analysis, multiple attractors coexistence, switching transients.
The reason for the self-similarity property of complex network is still an open issue. In this paper, we focus on the influence of degree, betweenness, and coreness on self-similarity of complex network. Some nodes are removed from the original network based on the definitions of degree, betweenness, and coreness in the ascending and descending order. And then, some new networks are obtained after removing nodes. The self-similarities of original network and new networks are compared. Moreover, two real networks are used for numerical simulation, including a USAir network and the yeast protein interaction (YPI) network. The effects of the three statistical variables on the two real networks are considered. The results reveal that the nodes with large degree and betweenness have great effects on self-similarity, and the influence of coreness on self-similarity is small.
A novel Filippov forest-pest system with threshold policy control (TPC) is established while an economic threshold (ET) is used to guide switching. The aim of our work is to address how to reasonably and successfully control pests by means of sliding dynamics for the Filippov system. On the basis of the above considerations, conditions for the existence and stability of equilibria of subsystems are addressed, and the sliding segments and several types of equilibria of the proposed system are defined. These equilibria include the regular/virtual equilibrium, pseudoequilibrium, boundary equilibrium, and tangent point. Further, not only are the relations between nullclines and equilibria of the Filippov system discussed, but the relations between pseudoequilibrium, nullclines, and the sliding segment are discussed. More importantly, four cases of sliding bifurcations of the Filippov system with respect to different types of equilibria of subsystems are investigated, and the corresponding biological implications concerning integrated pest management (IPM) are analyzed. Our results show that the points of intersection between nullclines are equilibria of the system, and the two endpoints of the sliding segment are on the nullclines. It is also verified that the pseudoequilibrium is the point of intersection of the sliding segment and nullclines of the Filippov system, and the pseudoequilibrium exists on the sliding segment. More interestingly, sliding dynamics analysis reveals that the Filippov system has sliding limit cycles, a bistable state and a stable refuge equilibrium point, and the optimal time and strategy for controlling pests are provided.
<abstract> <p>A periodically forced Filippov forest-pest model incorporating threshold policy control and integrated pest management is proposed. It is very natural and reasonable to introduce Filippov non-smooth system into the ecosystem since there were many disadvantageous factors in pest control at fixed time and the threshold control according to state variable showed rewarding characteristics. The main aim of this paper is to quest the association between pests dynamics and system parameters especially the economical threshold <italic>ET</italic>, the amplitude and frequency of periodic forcing term. From the view of pest control, if the maximum amplitude of the sliding periodic solution does not exceed economic injury level(<italic>EIL</italic>), the sliding periodic solution is a desired result for pest control. The Filippov forest-pest model exhibits the rich dynamic behaviors including multiple attractors coexistence, period-adding bifurcation, quasi-periodic feature and chaos. At certain frequency of periodic forcing, the varying system initial densities trigger the system state switch between different attractors with diverse amplitudes and periods. Besides, parameters sensitivity analysis shows that the pest could be controlled at a certain level by choosing suitable parameters.</p> </abstract>
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