Dissertation > Mathematical sciences and chemical > Mathematics > Algebra,number theory, portfolio theory > Differential algebra, differential algebra

The Application of Differential-algebraic Systems in Ecological Economics

Author ZhangGuoDong
Tutor ChenBoShan
School Hubei Normal University,
Course Applied Mathematics
Keywords Stability Hopf bifurcation Time delay Lyapunov function predator-prey Differential-algebraic system Mixed monotonellow
CLC O155
Type Master's thesis
Year 2011
Downloads 15
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The paper mainly studies the stability and Hopf bifurcation of a class of harvestingdifferential-algebraic ecological economic systems and consists of five chapters.The first chapter as an introduction, modeling process of the differential-algebraic eco-logical economic system, its real meaning, the current research status, the main work andinnovation of this paper have been Pointed out.In chapter 2, the stability and Hopf bifurcation of the harvesting differential-algebraicecological economic system without time delay are given by using the stability and bifurca-tion theory of differential-algebraic system, the conditions for stability of the positive equi-librium point are obtained, by making economic factor m as bifurcation parameter, we gotthe conditions of the existence and stability of Hopf bifurcation.In chapter 3, to the delayed harvesting differential-algebraic ecological economic sys-tem, its stability and Hopf bifurcation are given by using the normal form theory ofdifferential-algebraic system, the conditions for stability of the positive equilibrium pointare obtained, let time delayτas bifurcation parameter, the existence of Hopf bifurcation andthe direction of Hopf bifurcation are obtained.In the fourth chapter, we discussed the stability of the positive equilibrium point ofthe harvesting two Lotka-Volterra differential-algebraic ecological economic system basingon the normal form theory of differential-algebraic system and by constructing a properLyapunov function.In the fifth chapter, a class of differential-algebraic ecological economic system withharvesting is discussed, basing on the normal form theory of differential-algebraic systemand the theory of mixed monotone ?ow, some results about the uniqueness and stability ofthe positive equilibrium point are obtained.The conclusion is showed in the finally chapter, and some problems we need study laterare given.

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