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Global dynamics of Filippov‐type plant disease models with an interaction ratio threshold
Author(s) -
Li Wenxiu,
Huang Lihong,
Wang Jiafu
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6450
Subject(s) - mathematics , attractor , bounded function , type (biology) , saddle , orbit (dynamics) , control theory (sociology) , mathematical analysis , control (management) , mathematical optimization , computer science , ecology , biology , artificial intelligence , engineering , aerospace engineering
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.