We study the solutions to following Dirichlet boundary problem: d 2x(t) dt2 + λ f(x(t)) = 0, where x ∈ R, t R+, with conditions: x(0) x(1) A R. Especially we focus on varying parameters and in case phase plane representation of equation contains a saddle loop filled period annulus surrounding center. introduce concept mixed which take values above below A, generalizing well-studied positive sol...

Studying high-dimensional Hamiltonian systems with microstructure, it is an important and challenging problem to identify reduced macroscopic models that describe some effective dynamics on large spatial and temporal scales. This paper concerns the question how reasonable macroscopic Lagrangian and Hamiltonian structures can by derived from the microscopic system. In the first part we develop a...

In this paper, a multimachine power system is first represented as the generalized Hamiltonian control system with dissipation. Then, a decentralized saturated steam valving and excitation controller, which is staticly measurable, is proposed based on the Hamiltonian function method. Last, an example of threemachine power system is discussed in detail.

The tri-Hamiltonian method is applied to the Merola-Ragnisco-Tu equation. This enables us construct a new integrable system, whose continuum limit related AKNS system. Moreover, system proved have linear spectral problems (Lax pair), bi-Hamiltonian structure and Darboux-Bäcklund transformation. Through transformation, we some exact solutions for