Global dynamics of Filippov-type plant disease models with an interaction ratio threshold |
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Authors: | Wenxiu Li Lihong Huang Jiafu Wang |
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Affiliation: | 1. College of Mathematics and Econometrics, Hunan University, Changsha, 410082 Hunan, China;2. Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science and Technology, Changsha, 410114 Hunan, China |
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Abstract: | A Filippov-type plant disease model is developed by introducing a interaction ratio threshold, the number of susceptible plants infected by per diseased plant, which determines whether control measures including replanting or roguing are carried out. The main purpose of this paper is to give a completely qualitative analysis of the model. By employing Poincaré maps, our analysis reveals rich dynamics including a global attractor bounded by a touching closed orbit, which is convergent in finite time from its outside, a global attractor bounded by two touching closed orbits and a pseudo-saddle, and a globally asymptotically stable pseudo-node. Moreover, we give biological implications of our results in implementing control strategies for plant diseases. |
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Keywords: | Filippov type global attractor interaction ratio threshold Poincaré map |
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