Switching dynamics analysis of forest-pest model describing effects of external periodic disturbance

Yi Yang; Lirong Liu; Changcheng Xiang; Wenjie Qin; Yi Yang; Lirong Liu; Changcheng Xiang; Wenjie Qin

doi:10.3934/mbe.2020239

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 4: 4328-4347. doi: 10.3934/mbe.2020239

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Research article

Switching dynamics analysis of forest-pest model describing effects of external periodic disturbance

1.
College of Computer Science and Engineering, Chongqing Three Gorges University, Chongqing 404100, China
2.
Key Laboratory of Intelligent Information Processing and Control of Chongqing Municipal Institutions of Higher education, Chongqing Three Gorges University, Chongqing 404100, China
3.
School of Mathematics and Statistics, Hubei Minzu University, Enshi 445000, China
4.
Three Gorges Mathematical Research Center, China Three Gorges University, Yichang 443002, China

Received: 18 April 2020 Accepted: 10 June 2020 Published: 19 June 2020

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 ET, 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(EIL), 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.
- Filippov forest-pest system,
- integrated pest control,
- periodic forcing,
- bifurcation analysis,
- multiple attractors coexistence
Citation: Yi Yang, Lirong Liu, Changcheng Xiang, Wenjie Qin. Switching dynamics analysis of forest-pest model describing effects of external periodic disturbance[J]. Mathematical Biosciences and Engineering, 2020, 17(4): 4328-4347. doi: 10.3934/mbe.2020239

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Abstract

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 ET, 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(EIL), 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.

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