Abstract
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.
Highlights
Due to population communities are imbedded in environments with seasonal or periodic variations, periodic forces play the vital role in ecological systems [1], [2]
To investigate and verify the effects of periodic forcing on behavior in population communities, the basic problem needs to be addressed: how are the dynamic complexities of the system affected by the seasonal variations?
We mainly investigate the effects of periodic forces and threshold policy control (TPC) on the successful pest control, and complex dynamics of the Filippov system and real biological implications with respect to pest control are addressed
Summary
Due to population communities are imbedded in environments with seasonal or periodic variations, periodic forces play the vital role in ecological systems [1], [2]. Periodic forces have been extensively studied in preypredator models because of its impacts on the interactions between two populations (i.e., prey and predator) [3]–[5]. L. Liu et al.: Dynamics Analysis of Periodically Forced Filippov Holling II Prey-Predator Model. A periodically forced Filippov (or non-smooth) prey-predator system related to complex dynamics and switching transients has been investigated and can refer to [6]. We mainly investigate the effects of periodic forces and TPC on the successful pest control, and complex dynamics of the Filippov system and real biological implications with respect to pest control are addressed. The results reveal that the effects of switching transients on pest control associate with the amplitude of periodic forcing term and its frequency.
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