Periodicity hubs and spirals in an electrochemical oscillator

Discontinuous spirals of stability in an optically injected semiconductor laser

We report a new kind of discontinuous spiral with stable periodic orbits in the parameter space of an optically injected semiconductor laser model, which is a combination of the intercalation of fish-like and cuspidal-like structures (the two normal forms of complex cubic dynamics). The spiral has a tridimensional structure that rolls up in at least three directions. A turn of approximately 2π radians along the spiral and toward the center increases the number of peaks in the laser intensity by one, which does not occur when traversing the discontinuities. We show that as we vary the linewidth enhancement factor (α), discontinuities are created (destroyed) through disaggregation (collapses) from (into) the so-called shrimp-like structures. Future experimental verification and applications, as well as theoretical studies to explain its origin and relation with homoclinic spirals that exist in its neighborhood, are needed.

A numerical investigation of the effect of external resistance and applied potential on the distribution of periodicity and chaos in the anodic dissolution of nickel

Low density, elongation, and suppression of the shrimp-like structures in the resistance-potential phase diagrams have been observed in the oscillatory dissolution of nickel.

Nested arithmetic progressions of oscillatory phases in Olsen's enzyme reaction model

We report some regular organizations of stability phases discovered among self-sustained oscillations of a biochemical oscillator. The signature of such organizations is a nested arithmetic progression in the number of spikes of consecutive windows of periodic oscillations. In one of them, there is a main progression of windows whose consecutive number of spikes differs by one unit. Such windows are separated by a secondary progression of smaller windows whose number of spikes differs by two units. Another more complex progression involves a fan-like nested alternation of stability phases whose number of spikes seems to grow indefinitely and to accumulate methodically in cycles. Arithmetic progressions exist abundantly in several control parameter planes and can be observed by tuning just one among several possible rate constants governing the enzyme reaction.