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Dynamic Properties of a Differential-Algebraic Biological Economic System

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  • Hongyang Zhang
  • Chunrui Zhang

Abstract

We analyze a differential-algebraic biological economic system with time delay. The model has two different Holling functional responses. By considering time delay as bifurcation parameter, we find that there exists stability switches when delay varies, and the Hopf bifurcation occurs when delay passes through a sequence of critical values. Furthermore, we also consider the stability and direction of the Hopf bifurcation by applying the normal form theory and the center manifold theorem. Finally, using Matlab software, we do some numerical simulations to illustrate the effectiveness of our results.

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  • Hongyang Zhang & Chunrui Zhang, 2012. "Dynamic Properties of a Differential-Algebraic Biological Economic System," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-13, January.
    • Handle: RePEc:hin:jnljam:205346
    DOI: 10.1155/2012/205346
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