Qualitative analysis for a two-component peakon system with cubic nonlinearity

A Synthetical Two-Component Model with Peakon Solutions

A generalized two-component model with peakon solutions is proposed in this paper. It allows an arbitrary function to be involved in as well as including some existing integrable peakon equations as special reductions. The generalized two-component system is shown to possess Lax pair and infinitely many conservation laws. Bi-Hamiltonian structures and peakon interactions are discussed in detail...

Analysis of the Reliability of a Three-Component System with Two Repairmen

In this paper authors have considered a system having three units A, B1 and B2. A is controlled by a controller and B1 and B2 are independent. Two repairmen are involved in repair of the system. One of the repairmen (the first) is the foreman (boss) and the other an assistant (apprentice). Whenever any unit fails, repair is undertaken by boss. If the boss is busy in repairing and at the same ti...

Qualitative analysis on a cubic predator-prey system with diffusion

In this paper, we study a cubic predator-prey model with diffusion. We first establish the global stability of the trivial and nontrivial constant steady states for the reaction diffusion system, and then prove the existence and non-existence results concerning non-constant positive stationary solutions by using topological argument and the energy method, respectively.

Model-Independent Adaptive Control of Chua's System with cubic Nonlinearity

This paper proposes a linear adaptive state feedback controller which achieves asymptotic tracking of the controlled cubic Chua’s system. The gain vector is tuned using an adaptation law derived using the Lyapunov stability theory. The aim is to design an adaptive controller that mimics a predetermined input–output linearizing controller known for its effective performance in output tracking. W...

Undercompressive Shocks for a System of Hyperbolic Conservation Laws with Cubic Nonlinearity