Antiphase switching in arrays of globally coupled oscillators

摘要

A method and apparatus for accessing anti-phase states in a nonlinear system by globally coupling an array of oscillators. For N number of oscillators in the system, there are (N-1)! anti-phase (AP) states in phase space. AP states exist where each waveform is staggered out-of- phase with every other wave form. The system is controlled between AP states by means of a linear parameter and a hyper-switch. In an out-of- phase (OP) state the orbit remains on a basin boundary between or among AP states. As the linear parameter is decreased to a specific value, the orbit leaves the basin boundary and enters a canonical invariant region (CIR) towards an attractor. Each CIR contains one AP state and one attractor. Once the orbit has reached an attractor within the CIR it shall remain there until the linear parameter is increased and system again becomes unstable. Accordingly, by controlling the bias current in the system, the orbit may remain on the basin boundary until such time as the bias current is altered and forces the orbit into an invariant region thereby attaining an AP state. Furthermore, if the orbit is in a CIR, the bias current may be adjusted so that the system becomes unstable and returns to the basin boundary. This method of accessing different AP states in a system of globally coupled oscillators uses a hyperswitch together with control and release techniques for switching between or among AP states by pulsing a linear parameter.