Dissertation > Excellent graduate degree dissertation topics show

The Qualitative Analysis of the Biology System with Time Delay

Author: ZouLing
Tutor: XiongZuoLiang
School: Nanchang University
Course: Applied Mathematics
Keywords: predator-prey system eco-epidemic model time delay pest control asymptotically stability permanence Hopf bifurcation
CLC: O175
Type: Master's thesis
Year: 2011
Downloads: 25
Quote: 0
Read: Download Dissertation

Abstract


In this paper the population dynamics model and eco-epidemic model have been discussed, based on the traditional differential model, we adding in time delay, and thus we propose the differential equations with delay. This paper arranged as the following chapters:In the first chapter, the background and development of population dynamics system are given, and the major work of this paper is introduced.In the second chapter, the Hopf bifurcation of a predator-prey system has been studied which changes the roles of predator and prey when the prey becomes adult and with delay effect, we factor in age structure as the delay to establish the corresponding delay differential equations. We have discussed the system boundedness and persistence. By applying the theorem of Hopf bifurcation, Hopf bifurcation occurs as the delay crosses the critical value. Numerical simulation supported the academic results.In the third chapter, the persistence of an eco-epidemic model with distributed delay is investigated. Time delay plays an important role in eco-epidemic model; it may be affect the extinction and permanence. At last, sufficient condition of the permanence of the model is obtained.In chapter four, an eco-epidemic model with infinite delay and integrated pest management is proposed, the sufficient conditions for the stability of pest eradication periodic solution and permanence of the system are obtained by using Floquet’s theory and then rich dynamic phenomena such as bifurcation and chaos and so on was showed by numerical simulation.

Related Dissertations

  1. Robust Model Predictive Control of Networked Systems,TP273
  2. Robust Filter Design Based on Polynomially Parameter-dependent Lyapunov Functions,TP13
  3. Stability Analysis and Robust Controller Design for Stochastic Time-Delay Systems,TP13
  4. Stability Analysis of Systems with Time Delays,TP13
  5. Arthropod Diversity in Non-Crop Habitats at Margins of Paddy Fields of Different Types,S435.112
  6. Researches on System Control Theories and Their Applications of AUVs,TP13
  7. With Delay fishing items and based on the ratio of prey - predator model,O175
  8. Research of Robust Control for Uncertain Time-delay Singular Bilinear Systems,TP13
  9. Hot Galvanized Line Air Knife Control Research,TP273
  10. Studies on Exploitation of Beauveria Bassiana Production and Control of Tow Main Pests,S476.1
  11. ESPRIT Parameter Estimation Algorithm in Wideband Channel System,TN925
  12. Shenyang green pest expert advisory system establishment,S436.8
  13. A class of Epidemic Model with Age Structure Qualitative Analysis,O175
  14. Heilongjiang Province shelterbelts pests and diseases prevention and control characteristics and technology research,S763.7
  15. Moving Base Transfer Alignment Error Analysis and Compensation Method,V249.322
  16. The Qualitative Analysis of a Fast-Slow Predator-Prey System,O175
  17. Research on Tobacco Pest Control Network Information System,S435.72
  18. Robust H_∞ Control for Uncertain Time-delay Systems,TP13
  19. A Study on the Uncertainituy Time Delay System by Robust Control Theory,TP13
  20. Research on Analysis and Correction of Error Sources in Range and Doppler Tracking Data for Deep Space Vehicles,P228.4
  21. A ratio dependent on Three Species Food Chain Model Chaos Control and Research branch,O415.5

CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Differential equations, integral equations
© 2012 www.DissertationTopic.Net  Mobile