Abstract
The gradient representation and the fractional gradient representation with order α=2 of the Birkhoff system are studied. Firstly, the condition under which the Birkhoff system could be considered as a general gradient system is given. Secondly, the condition under which the system could be considered as a fractional gradient system with order α=2 is also obtained. For a gradient system, one could study its stability by using the Lyapunov theorem when its potential function V can be chosen as a Lyapunov function. Another, since the roots of characteristic equation of linearized system of the gradient system are real, then the stability of the system can be discussed by the Lyapunov's first-order approximate theory. Finally, two examples are given to illustrate the application of the results.
| Original language | English |
|---|---|
| Pages (from-to) | 1298-1300 |
| Number of pages | 3 |
| Journal | Beijing Ligong Daxue Xuebao/Transaction of Beijing Institute of Technology |
| Volume | 32 |
| Issue number | 12 |
| Publication status | Published - Dec 2012 |
Keywords
- Birkhoff system
- Fractional dynamics
- Gradient