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Bifurcations and Periodic Solutions for an Algae‐Fish Semicontinuous System

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  • Chuanjun Dai
  • Min Zhao
  • Lansun Chen

Abstract

We propose an algae‐fish semicontinuous system for the Zeya Reservoir to study the control of algae, including biological and chemical controls. The bifurcation and periodic solutions of the system were studied using a Poincaré map and a geometric method. The existence of order‐1 periodic solution of the system is discussed. Based on previous analysis, we investigated the change in the location of the order‐1 periodic solution with variable parameters and we described the transcritical bifurcation of the system. Finally, we provided a series of numerical results to illustrate the feasibility of the theoretical results. These results may help to facilitate a better understanding of algal control in the Zeya Reservoir.

Suggested Citation

  • Chuanjun Dai & Min Zhao & Lansun Chen, 2013. "Bifurcations and Periodic Solutions for an Algae‐Fish Semicontinuous System," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:619721
    DOI: 10.1155/2013/619721
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    References listed on IDEAS

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    1. Yuanfu Shao & Peiluan Li & Guoqiang Tang, 2012. "Dynamic Analysis of an Impulsive Predator-Prey Model with Disease in Prey and Ivlev-Type Functional Response," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-20, August.
    2. Hunki Baek & Younghae Do, 2009. "Seasonal Effects on a Beddington-DeAngelis Type Predator-Prey System with Impulsive Perturbations," Abstract and Applied Analysis, Hindawi, vol. 2009, pages 1-19, October.
    3. Yuanfu Shao & Peiluan Li & Guoqiang Tang, 2012. "Dynamic Analysis of an Impulsive Predator‐Prey Model with Disease in Prey and Ivlev‐Type Functional Response," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    4. Chuanjun Dai & Min Zhao & Lansun Chen, 2012. "Dynamic Complexity of an Ivlev-Type Prey-Predator System with Impulsive State Feedback Control," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-17, August.
    5. Chuanjun Dai & Min Zhao & Lansun Chen, 2012. "Dynamic Complexity of an Ivlev‐Type Prey‐Predator System with Impulsive State Feedback Control," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    6. Hunki Baek & Younghae Do, 2009. "Seasonal Effects on a Beddington‐DeAngelis Type Predator‐Prey System with Impulsive Perturbations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2009(1).
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