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Analysis and Control of the Singular System Model of Aphid Ecosystems

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  • Jingna Liu
  • Tie Zhang
  • Lichun Zhao
  • Bing Liu
  • Xueying Wei

Abstract

Considering the change of the parameter related to the natural enemy population and the impact on the aphid populations in the fold catastrophe manifold, the singular system model of aphid ecosystems is proposed. Combining singular system theory with catastrophe theory, the corresponding dynamics behaviors and the existence conditions of the impasse points are given by using the qualitative analysis. The biological significance of the analytical results is also discussed. The controllers are designed to make the aphid populations stabilize the refuge level by releasing natural enemy. Some numerical simulations are carried out to prove the results.

Suggested Citation

  • Jingna Liu & Tie Zhang & Lichun Zhao & Bing Liu & Xueying Wei, 2018. "Analysis and Control of the Singular System Model of Aphid Ecosystems," Mathematical Problems in Engineering, Hindawi, vol. 2018, pages 1-10, February.
    • Handle: RePEc:hin:jnlmpe:3030723
    DOI: 10.1155/2018/3030723
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