Control and synchronization of homoclinic chaos and its implication for neurodynamics

Homoclinic spike trains have been intensively investigated for single mode C02 lasers [1]; however, their occurrence has a more general significance insofar as this scenario fits the main aspects of action potentials in neurons.Stabilizing homoclinic trains has therefore a relevance for neural communication and synchronization, which seems to be the universal time code for perceptions. The core dynamics of homoclinic chaos is represented by the passage through a saddle point, in which neighbourhood the system susceptibility (response to an external perturbation) is veryhigh [21 and hence it is very easy to apply a control [1• A few aspects of regularization of homoclinic chaos are covered, such as, synchronization by an external pace-maker [4], DSS (delayed self-synchronization) [5], bursting [6],and MS (noise induced synchronization) [7]. Such a general scenario is compared with specific neurodynamic models;moreover its impact on communicating with chaos is discussed [8].Homoclinic chaos of the Shilnikov type, initially observed in laser experiments [1], shows striking similarities with theelectrical spike trains traveling on the axons of animal neurons [9]. More generally, chemical oscillators based on anactivator-inhibitor competition, which rule biological clocks controlling living rhythms, such as the heart pacemaker,hormone production, metabolism etc., are subject to frequency fluctuations of homoclinic type, since in general theycan not be reduced to a two dimensional dynamics, as done in artificial clocks in order to have stable limit cycles[2].Experimental evidence of synchronization on a laser operating in a homoclinic chaos regime is provided by adding asmall periodic modulation of a control parameter. Take a single mode CO2 laser with an intracavity electro-optic lossmodulator, driven by the voltage of a detector exposed to the laser intensity; the voltage passes through an amplifier ofgain R an it is summed to a fixed bias voltage B.The two control parameters (R and B) are set in a region where the laser intensity shows homoclinic chaos. The laserintensity displays a large spike above zero followed by a fast damped train of a few oscillations and a successive longer