Resonance effects determine the frequency of bursting Ca2+ oscillations

Dynamics of in-phase and anti-phase bursting in the coupled pre-Bötzinger complex cells

Activity of neurons in the pre-Bötzinger complex within the mammalian brain stem has an important role in the generation of respiratory rhythms. Previous experimental results have shown that the dynamics of sodium and calcium within each cell may be responsible for various bursting mechanisms. In this paper, we study the bursting dynamics of the two-coupled pre-Bötzinger complex neurons. Using a combination of fast-slow decomposition and two-parameter bifurcation analysis, we explore the possible forms of dynamics that the model network can produce as well the transitions of in-phase and anti-phase bursting respectively.

Amplification of information transfer in excitable systems that reside in a steady state near a bifurcation point to complex oscillatory behavior

We study the amplification of information transfer in excitable systems. We show that excitable systems residing in a steady state near a bifurcation point to complex oscillatory behavior incorporate several frequencies that can be exploited for a resonant amplification of information transfer. In particular, for excitable neurons that reside in a steady state near a bifurcation point to elliptic bursting oscillations, we show that in addition to the resonant frequency of damped oscillations around the stable focus, another frequency exists that resonantly enhances large amplitude bursts and thus amplifies the information transfer in the system. This additional frequency cannot be found by the local stability analysis and has never been used for amplifying the information transfer in a system. The results obtained for elliptic bursting oscillations can be generalized also to other complex oscillators, such as parabolic or square-wave bursters. Additionally, the biological importance of presented results in the field of neuroscience is outlined.

Detecting and controlling unstable periodic orbits that are not part of a chaotic attractor

A method for controlling unstable periodic orbits (UPOs) that have not been controllable before is presented. The method is based on detecting UPOs that are situated outside the skeleton of a chaotic attractor. The main idea is to exploit flexible parts of the attractor, which under weak external perturbations allow variable excursions of the trajectory away from its originally determined path. After the perturbation, the trajectory of the autonomous system seeks its path back to the chaotic attractor and reveals additional UPOs that are otherwise not used by the system. It is shown that these UPOs can be controlled as easily as the UPOs that form the basic chaotic attractor. The effectiveness of the proposed method is demonstrated on two different chaotic systems with very distinct response abilities to external perturbations. Additionally, some applications of the method in the fields of laser technology, information encoding, and biomedical engineering are discussed.