Subcritical modulational instability and transition to chaos from periodicity

A Universal Transition from Quasi-periodicity to Chaos

A common route to chaos in dissipative systems proceeds from periodic to quasi-periodic flow (with two independent frequencies). Then, in the absence of rotational symmetry, the system generally mode locks before becoming turbulent. Beyond these qualitative features, the numerous experiments that have examined this regime differ in detail. Dynamical system theory had made the occurrence of the ...

General approach to spatiotemporal modulational instability processes

Variational approach to the modulational instability.

We study the modulational stability of the nonlinear Schrödinger equation using a time-dependent variational approach. Within this framework, we derive ordinary differential equations (ODE's) for the time evolution of the amplitude and phase of modulational perturbations. Analyzing the ensuing ODE's, we rederive the classical modulational instability criterion. The case (relevant to application...

Transition from Periodicity to Chaos in a PWM-Controlled buck converter with Zad Strategy

The transition from periodicity to chaos in a DC-DC Buck power converter is studied in this paper. The converter is controlled through a direct Pulse Width Modulation (PWM) in order to regulate the error dynamics at zero. Results show robustness with low output error and a fixed switching frequency. Furthermore, some rich dynamics appear as the constant associated with the first order error dyn...

Modulational instability of spinor condensates

We demonstrate, analytically and numerically, that the ferromagnetic phase of the spinor Bose-Einstein condenstate may experience modulational instability of the ground state leading to a fragmentation of the spin domains. Together with other nonlinear effects in the atomic optics of ultra-cold gases (such as coherent photoassociation and four-wave mixing) this effect provides one more analogy ...