Instant Dynamics Research Articles

Functional Responses of Autaptic Neural Circuits to Acoustic Signals

It is important for functional neurons of animals or human beings to adapt to external stimuli, such as sound, pressure, and light. Regarding this aspect, autaptic neuron enables itself to utilize historical information to modulate its instant dynamics, such that it may be able to behave adaptively. In this paper, a FitzHugh–Nagumo based autaptic neuron is employed to investigate the capability of a sound-sensitive neural circuit’s adaptation and filtering to analog acoustic signals. Extensive simulations are performed for excitatory and inhibitory types of autaptic neurons. The results show that the time-delayed feedback of the excitatory chemical autapse can be tuned to play the role of a narrow-band filter in response to a broadband acoustic signal. While the excitatory chemical autaptic neuron cannot saturate its response amplitude due to its positive feedback gain, the inhibitory chemical autapse can drive the neuron’s amplitude to converge as the intensity of external drive increases, which reveals the capability of adaptation. What’s more, the inhibitory chemical autaptic neuron can also exhibit a novel bursting adaptation, in which the number of spikings contained in one bursting changes as the electrical activity evolves. For electrical autaptic neurons, it is also found that both time-delay feedback gains can effectively modulate the response of neuron to acoustic signal. While the variation of time-lags mainly changes the spiking rates of the excitatory electrical autaptic neuron, the feedback gain alters its response amplitude. Lastly, by carefully tuning the time-lags, the expected subthreshold dynamics for larger inhibitory feedback gains can be switched to nearby quasi-periodic firings, which implies a competing relation between the time-delays and the feedback gains in the spiking dynamics of the inhibitory electrical autaptic neurons. The diverse emerging phenomena are expected to facilitate the design of online or interactive learning artificial neural networks with these functional autaptic neurons.

Interpolating between instant and light front dynamics

The “instant” and “light front” forms of relativistic dynamics postulated by Dirac refer to physical conditions on flat spacelike surfaces in the Minkowski space. We consider another flat surface in the Minkowski space that upon parametric rotation interpolates between “instant” and “light front” surfaces. A projection of the covariant perturbation theory on the new surface is then considered. One limit of the theory reproduces the usual instant dynamics, whereas a different limit gives a light front dynamics. Neither infinite momemtum frame limit nor infinite momenta are involved. Although the interpolating surface is the “instant” surface in the moving system of reference, we argue why our procedure should not be associated with a Lorentz transformation.