Dissertation > Excellent graduate degree dissertation topics show

Dynamical System Analysis on Two Classes of Second-Order Quadratic Difference Equation

Author: WangJieQun
Tutor: GuEnGuo
School: Central South University for Nationalities
Course: Applied Mathematics
Keywords: difference equations stability critical set global bifurcation singular set attractor
CLC: O175.7
Type: Master's thesis
Year: 2011
Downloads: 26
Quote: 0
Read: Download Dissertation

Abstract


In this paper, in connection with different situations of parameters of the common second-order difference equation, we can simplify it into two different types of nonlinear mapping systems for research and discussion. The two types of nonlinear mapping system of local dynamics properties and global dynamics are mainly analyzed. First, we should study this article a brief overview of the problems as well as some related research status and background, and explained the relevant concepts related to this article and basic theoretical knowledge in order to study the problem we have a preliminary understanding and awareness. Second, two types of mapping system were analyzed and researched by making use of mainly the theory of critical curves and prefocal curves of focal point.According to a class of second-order difference equations changed into noninvertible iteration map, its dynamic behavior is investigated by using of two-dimensional irreversible continuous iteration mapping dynamic system theory. Firstly, the stability and the local bifurcations of the fixed points are analyzed, and then the global bifurcations of the basin of all bounded attractors for the mapping system are studied by critical set theory of irreversible iteration map.According to the class of second-order difference equations changed into nonlinear mapping system with a vanishing denominator, Firstly, the stability and the local bifurcations of the fixed points are analyzed. Finally, the structures of attractor and topological structures of the basin for the mapping system are studied and explained by singular set theory with a vanishing denominator.Finally, on the basis of different situations of other parameters of the common second-order difference equation, we can simplify into its various other nonlinear mapping system, and on this basis as we pointed out the direction for further discussion and research.

Related Dissertations

  1. Analysis and Study of Abutment Stability in Concrete High Arch Dam by Three-Dimensional Nonlinear Finite Element Method,TV642.4
  2. The Study on Structural Calculation and Analysis Method of Lattice-type Crane with Variable Cross-section Boom,TH21
  3. Power System Dynamic Voltage Stability Simulation Study Based on Precise Integration Method,TM712
  4. Simulation and Analysis about Switched Reluctance Generator Power Supply System,TM31
  5. Research and Design for the Laser’s Power Control System of Laser Direct Writing,TN249
  6. Stability Analysis of Systems with Time Delays,TP13
  7. Research on Input-To-State Stability of Discrete-Time Nonlinear Systems,TP13
  8. Astudy on Samuel Huntington’s Theory of Political Stability,D09
  9. Stability Analysis of Roller Compacted Concrete Gravity Dam Based on Time-history Method,TV642.2
  10. Thermal Stability of Complexes of Chitosan Quaternary Ammonium Salt and Metal Ion,O634
  11. Synthesis and Application of the chloro- methoxy fatty acid methyl esters,TQ414.8
  12. Research on Anti-periodic Solutions of Delayed Cellular Neural Networks without Assuming Global Lipschitz Conditions,TP183
  13. Investigations on Related Problems of the Integrable Coupling Systems and the Exact Solutions of Nonlinear Differential-Difference Equations,O175.7
  14. The Existence of Uniform Attractor for A Class of Non-autonomous Wave Equation,O175
  15. The DNA Cloning and RNA Interference of Some Functional Genes in Laodelphax Striatellus (Fallen),S435.112.3
  16. Study of Legal Safeguard Mechanism on Financial Stability,F832.2
  17. To Promote the Healthy Development of the Stock Market Stability Tax System Conception,F812.42
  18. Dynamics of Unstable Linear Systems under Unbalanced Delta-Modulated Feedback Control,O231
  19. Piecewise continuous numerical stability of delay differential equations,O175
  20. Study on the Tactics of Ideological and Political Education to Maintain the Stability in Xinjiang,D67
  21. Design and Analysis of Model-free Controller for a Class of Nonlinear System,TP273

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