Complexity Induced by External Stimulations in a Neural Network System with Time Delay

Complexity and dynamical analysis in neural systems play an important role in the application of optimization problem and associative memory. In this paper, we establish a delayed neural system with external stimulations. The complex dynamical behaviors induced by external simulations are investigated employing theoretical analysis and numerical simulation. Firstly, we illustrate number of equilibria by the saddle-node bifurcation of nontrivial equilibria. It implies that the neural system has one/three equilibria for the external stimulation. Then, analyzing characteristic equation to find Hopf bifurcation, we obtain the equilibrium’s stability and illustrate periodic activity induced by the external stimulations and time delay. The neural system exhibits a periodic activity with the increased delay. Further, the external stimulations can induce and suppress the periodic activity. The system dynamics can be transformed from quiescent state (i.e., the stable equilibrium) to periodic activity and then quiescent state with stimulation increasing. Finally, inspired by ubiquitous rhythm in living organisms, we introduce periodic stimulations with low frequency as rhythm activity from sensory organs and other regions. The neural system subjected by the periodic stimulations exhibits some interesting activities, such as periodic spiking, subthreshold oscillation, and bursting-like activity. Moreover, the subthreshold oscillation can switch its position with delay increasing. The neural system may employ time delay to realize Winner-Take-All functionality.

Dynamics of Input Patterns Modulate the Behavior of a Model of Olfactory Bulb Function

Input patterns to the olfactory bulb are dynamic and change in an odor-specific manner as measured by selective calcium imaging of olfactory bulb input. To our knowledge, none of the published models of olfactory bulb function uses dynamic input patterns. Therefore we tested how dynamic input alters the behavior of a simple model consisting of two layers. The membrane potential of the first-layer neurons, integrate-and-fire neurons corresponding to mitral cells, was modulated with a subthreshold oscillation at respiration frequency. The membrane potential of the second-layer neurons was used to discriminate input patterns. We implemented oscillating input with amplitudes and latencies different for each mitral cell. Not only varying the input amplitudes but also de-synchronizing the input, and varying the relation between latency and input amplitude, individually changed the model's performance significantly. The discrimination time was affected more easily than the number of second-layer neurons that can differentiate an odor pair. Increasing the de-synchronization, i.e., the spread of latency values, reduced the differences in response time between strong and weak stimulus pairs without reducing the number of reacting cells. Input phase relative to the subthreshold oscillation altered the effect of de-synchronization. Thus dynamic input changes performance parameters of models of olfactory information processing that can be verified experimentally.

Oscillation and Repetitive Firing in Squid Axons

Space-clamped squid axons treated with low calcium and computed Hodgkin-Huxley (HH) axons were stimulated by steps of superthreshold current from 101 to 400% of the rheobasic value over a temperature range of 5–27°C. The natural frequency of sustained repetitive firing of real and computed axons depended weakly upon stimulus intensity and strongly upon temperature, with a Q10 of 2.7 (experimental) and 2.6 (computed). For real axons, but not the computed axon, the intervals between the first two spikes were shorter than between subsequent spikes. Constant spike frequencies from 75 Hz at low intensities and temperatures to 330 Hz at high intensities and temperatures were soon achieved. Subthreshold and superthreshold responses were sometimes intermixed in a train of responses from a real axon responding to a constant step of current, but not predicted by HH. The time interval following a spike was always longer than that following a subthreshold oscillation in slightly decalcified real axons, as Huxley and FitzHugh also found for computed axons. There was a bias toward spikes at the beginning of the train and toward subthreshold responses later on. Some repeated patterns were found, every second, third, or fourth response being a spike. Neither the HH equations nor the computed or experimental threshold behaviors show a critical temperature to support a membrane phase transition.