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- Synchronization (1)
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We investigate different dynamical regimes of neuronal network in the CA3 area of the hippocampus.
The proposed neuronal circuit includes two fast- and two slowly-spiking cells which are interconnected by means of dynamical synapses. On the individual level, each neuron is modeled by FitzHugh-Nagumo equations. Three basic rhythmic patterns are observed: gamma-rhythm in which the fast neurons are uniformly spiking, theta-rhythm in which the individual spikes are separated by quiet epochs, and theta/gamma rhythm with repeated patches of spikes. We analyze the influence of asymmetry of synaptic strengths on the synchronization in the network and demonstrate that
strong asymmetry reduces the variety of available dynamical states. The model network exhibits multistability; this results in occurrence of hysteresis in dependence on the conductances of individual connections. We show that switching between different rhythmic patterns in the network
depends on the degree of synchronization between the slow cells.
In a strong constant electric field, a dielectric particle
immersed in a weakly conducting fluid exhibits spontaneous rotations. This phenomenon is known under the name of the Quincke effect. In the original setup the particle was suspended on a silk thread and performed torsional oscillations of remarkably high amplitude.
We derive the governing equations for this experiment, and
ascertain that onset of oscillations from the quiescent state corresponds to the supercritical Hopf bifurcation.
For the case of a soft thread, we characterize the regime of large-scale torsional relaxation oscillations: explicit estimates are derived for their period and amplitude,
effects of bifurcation delay are described. In a stronger electric field, these relaxation oscillations yield to small-scale erratic rotations of the pendulum.
In a strong constant electric field, a dielectric particle immersed in a weakly conducting fluid exhibits spontaneous rotations. This phenomenon is known under the name of the Quincke effect. In the original setup the particle was suspended on a silk thread and performed torsional oscillations of remarkably high amplitude. We derive the governing equations for this experiment, and ascertain
that onset of oscillations from the quiescent state corresponds to the supercritical Hopf bifurcation.
For the case of a soft thread, we characterize the regime of large-scale torsional relaxation oscillations:
explicit estimates are derived for their period and amplitude, effects of bifurcation delay are described. In a stronger electric field, these relaxation oscillations yield to small-scale erratic rotations of the pendulum.