We investigate the possibility that the large mixing of neutrinos is induced by their large coupling to a five-dimensional bulk neutrino. In the strong coupling limit the model is exactly soluble. It gives rise to an oscillation amplitude whose squared-mass difference is independent of the channel, thus making it impossible to explain both the solar and the atmospheric neutrino oscillations sim...

We consider the Liénard equation and we give a sufficient condition to ensure existence and uniqueness of limit cycles. We compare our result with some other existing ones and we give some applications.

Article history: Received 6 November 2009 Received in revised form 14 February 2010 Accepted 15 February 2010 Available online 19 February 2010 Communicated by C.R. Doering

Errors are found in example problems from Henri Poincaré’s paper “Mémoire sur les courbes définies par une équation différentielle.” Examples four and five from chapter seven and examples one, two, and three from chapter nine do not have the limit cycles at infinity predicted by Poincaré. Instead they have fixed points at every point at infinity. In order to understand the errors made by Poinca...

This chapter introduces the paradigm `Limit Cycle Walking'. This paradigm for the design and control of two-legged walking robots can lead to unprecedented performance in terms of speed, efficiency, disturbance rejection and versatility. This is possible because this paradigm imposes fewer artificial constraints to the robot's walking motion compared to other existing paradigms. The application...

Legged passive dynamic systems that can exhibit a periodic gait that is inherently stable, provide highly desirable templates for the creation of robust legged robotic systems. However, even if a stable limit cycle exists, the system will be unable to recover if a disturbance is large enough. Hence it would be useful to know exactly which states evolve towards the limit cycle and which states l...

This paper shows how globally attractive limit cycle oscillations can be induced in a system with a nonlinear feedback element. Based on the same principle as the Van der Pol oscillator, the feedback behaves as a negative damping for low velocities but as an ordinary damper for high velocities. This nonlinear damper can be physically implemented with a continuous variable transmission and a spr...