Complexity dynamics and simulations in a discrete switching ecosystem induced by an intermittent threshold control strategy

Xinli Hu; Wenjie Qin; Marco Tosato

doi:10.3934/mbe.2020115

Mathematical Biosciences and Engineering, 2020, 17(3): 2164-2178. doi: 10.3934/mbe.2020115. Research article

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Complexity dynamics and simulations in a discrete switching ecosystem induced by an intermittent threshold control strategy

Xinli Hu, Wenjie Qin, Marco Tosato

1 School of Science, Xi’an Polytechnic University, Xi’an 710048, China
2 Three Gorges Mathematical Research Center, China Three Gorges University, Yichang 443002, China
3 Laboratory for Industrial and Applied Mathematics, York University, Toronto, M3J 1P3, Canada

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Pest control is a worldwide challenge. An approach that has been developed to meet this challenge is the integrated pest management (IPM) strategy, which aims to offer environmentally sensitive solutions to pest problems, and takes into account the complex dynamics involved in the design of controlling pests. In this paper, we propose a discrete switching host-parasitoid model with a threshold control strategy, meanwhile, provide some qualitative analyses of the complexity of dynamic behaviors of the model that includes single and multi-parameter bifurcations and chaos. Furthermore, we do some numerical bifurcations and parameter sensibility analysis, revealing how the key control parameters and initial interaction state between the two populations affect pest control, as well as the dynamical balance between of the hosts and parasitoids. The model and analytical techniques developed in this work could be applied in other settings relevant to threshold control strategies.

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Keywords: switching model; pest control; threshold policy; multiple coexisting attractors; dynamic complexity

Citation: Xinli Hu, Wenjie Qin, Marco Tosato. Complexity dynamics and simulations in a discrete switching ecosystem induced by an intermittent threshold control strategy. Mathematical Biosciences and Engineering, 2020, 17(3): 2164-2178. doi: 10.3934/mbe.2020115

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