Dissertation > Excellent graduate degree dissertation topics show

Research on Several Problems of Planar Piecewise-linear Dynamical Systems

Author: XuBin
Tutor: YangLiJun
School: Tsinghua University
Course: Mathematics
Keywords: piecewise-smooth homoclinic bifurcation Filippov system Poincare′map
CLC: O19
Type: Master's thesis
Year: 2013
Downloads: 7
Quote: 0
Read: Download Dissertation

Abstract


Non-smooth systems consist of piecewise smooth systems, the Filippov systems andhybrid systems. After hundreds of years of study, there are plenty of results on smoothdynamical systems; but non-smooth systems have emerged only in recent decades, andthere remain many issues to be studied. Non-smooth systems have many applications,such as machinery, circuit, control systems, etc. Therefore, the non-smooth systems haveimportant theoretical significance and wide application prospects.In this dissertation, we mainly study the existence of homoclinic orbits and the ho-moclinic bifurcations in planar piecewise-linear system. We will first introduce severalexisting research results on piecewise smooth systems, including boundary equilibriumbifurcations, periodic orbits and Hopf bifurcations. The existence of homoclinic orbit inthis system can be divided into two cases, one is a system formed by a visible saddle pointsand a visible focus (or a center), the other one is a system formed by the coincidence of theoriginal point and two nodes with inverse stability.In view of the two cases, we provide thenecessary and sufcient conditions for the existence of homoclinic orbit, and then analyzethe homoclinic bifurcation. Finally, we provide the Poincare′map of periobic orbits inFilippov system, based on which we can do some further study on the existence, stabilityand isolation of periodic orbits.

Related Dissertations

  1. Periodic Solution and Stick-Slip Bifurcation for A Class of Systems with Dry Friction,O242.1
  2. Bifurcation and Chaos of Functionally Graded Materials Circular Plates,O322
  3. Bifurcation Analysis of Predator-Prey Models with Nonmonotonic Functional Response,O175
  4. The Positive Periodic Solutions of N-dimensional Periodic Population Dynamical Systems with Impulse,O175
  5. Limit Cycles of a Lienard System,O175.12
  6. Periodic Solutions of Elastic Impact Oscillators of Superlinear Time-Weight Equations,O302
  7. Qualitative Analysis of a SIRS Model,O193
  8. Dynamic Behavior of Rotor System Supported on Magnetic Bearings,O322
  9. Bifurcation analysis of the types of planar polynomial systems,O193
  10. About the Incidence Function of SIRS Infectious Disease Model,O193
  11. Nonlinear Vibration and Bifurcation Analysis for Rotor-Bearing-Seal Systems,O347.6
  12. Qualitative Analysis of Several Categories Higher Polynomial Systems,O175.12
  13. Different external excitation Duffing system's global dynamics simulation and analysis,O322
  14. Research on Symmetric/Asymmetric Bifurcation and Chaos of Lateral Motion of Railway Passegner Car System,O415.5
  15. Dynamical Behaviors of Some Differential, Difference Equations,O175
  16. A Study on the Catastrophe and the Chaotic Motion of Shallow Shells under Pressure and Temperature and Transverse Periodic Load,TU33
  17. The Nonlinear Analysis on the Mechanism Giving Rise to the Oil Whip Instability of Large High-Speed Rotor,TH113.1
  18. Study on Some Nonlinear Dynamics Problems of Rotor System with Impact-rubbing,TH113.1
  19. Research on the Analysis Method of Mechanical Fault Signal Based on Topology Contravariant and Its Application,TH17
  20. Bifurcation of Several Kinds of Differential Equations,O175
  21. Research on Bifurcation, Chaos and Control of Three Types of High Dimensional Systems,O175

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