Dissertation > Excellent graduate degree dissertation topics show

Harmonics and Bifurcations of Harmonics and Chaos in Duffing Equation

Author: CaiMeiXiang
Tutor: JingZhuJun
School: Hunan Normal University
Course: Basic mathematics
Keywords: Duffing equation Melnikov method Secondary average method Branch Chaos
CLC: O19
Type: Master's thesis
Year: 2006
Downloads: 105
Quote: 0
Read: Download Dissertation

Abstract


In this paper, the local bifurcation theory of dynamical systems , second-order averaging method and the Melnikov theory and chaos theory , research with five restoring force , an external force , and a difference between the dynamic behavior of the Duffing equation . Currently, very little research on the difference between the impact of dynamic . The quadratic average method given harmonic solutions , the conditions for the existence and the branch of the second-order harmonic solutions , third-order harmonic solutions , as well as second-order Transdimensional harmonic solutions . The application of the Melnikov method to analyze m ( m gt; 3 ) order harmonic solutions and chaotic conditions for the existence . Verify these theoretical results by numerical simulations , including bifurcation diagram bifurcation surfaces phase diagram , and find a new dynamic behavior , which include chaos suddenly appeared and suddenly converge to the cycle -1 rails , chaos suddenly disappear , chaos along the and dual-band chaos lead to chaos, chaos in the area of complex periodic windows ( including the cycle -2,3,5 ) , interior crisis (interior crisis), the boundary crisis (boundary crisis) and cycle -1 ,2,3 -fold branch the complex dynamics of the cycle 3 bubble (period-3 bubble) . The paper is divided into two chapters . Chapter a brief introduction of the local branch of the continuous dynamic systems theory , the average second-order theory and Melnikov theory . The second chapter with five recovery force , a complex dynamic behavior of the external force , and a difference between the Duffing equation , given the the cycle perturbations system produce saddle- node bifurcation, super ( ) bifurcation and chaotic motion conditions , the use of numerical simulation method to verify the theoretical analysis results , and find a new complex and dynamic .

Related Dissertations

  1. The Study and Application of the Generalized Hamiltonian System with Spherical Foliation Structure,O175
  2. Heilongjiang Unified Marketing of Instant Noodles,F274
  3. Studies on Shoot Treating and Top Grafting Technique for Replacing Cultivar of Pear Tree,S661.2
  4. The Expression and Mechanism of NF-κ B and IL-6 after 90% Portal Vein Ligation in Rats,R657.3
  5. Genetic Analysis and QTL Mapping for Primary Branch Angle in a Rice (Oryza Sativa L) RIL Population,S511.22
  6. College Graduation Party Construction graders,D267.6
  7. Bank of China, Gansu Branch of Economic Capital Management,F832.2
  8. Study on Legal Aspects of Electronic Commerce Development & Application,D923.6
  9. Two Algorithms for Image Processing Based on Chaos and Fractal,TP391.41
  10. Research and Implement of Self-adaptive Image Encryption Algorithm Based on Chaos,TP309.7
  11. Deformation Analysis and Prediction Based on Chaotic Time Series,N945.2
  12. Bifurcation and Chaos of Functionally Graded Materials Circular Plates,O322
  13. Numerical Study of Stochastic Supersensitiviy of Generalized Burgers Equation,O241
  14. Stability Analysis of Helicopter Rotor Flapping,V224
  15. Study on Forecasting Methods of Rolling Bearing Friction Torque,TH133.33
  16. Preliminary Study on Law Dimension and Visualization of Nonlinear System,TP391.41
  17. The Study of Dynamic Competition Strategy on Trade Financing Services in the Hunan Branch, Bank of China,F740.45
  18. Chaotic Network File System password,TN918.2
  19. Based on Chaos Theory traffic time series prediction,TN915.09
  20. The Group Restaurant Management System Design and Implementation,TP311.52
  21. Digital Image Encryption and Encryption Algorithm Performance Evaluation,TP391.41

CLC: > Mathematical sciences and chemical > Mathematics > Dynamical systems theory
© 2012 www.DissertationTopic.Net  Mobile