Oscillatority of Nonlinear Systems with Static Feedback

New Lyapunov-like conditions for oscillatority of dynamical systems in the sense of Yakubovich are proposed. Unlike previous results these conditions are applicable to nonlinear systems and allow for consideration of nonperiodic, e.g., chaotic modes. Upper and lower bounds for oscillations amplitude are obtained. The relation between the oscillatority bounds and excitability indices for the systems with the input are established. Control design procedure providing nonlinear systems with oscillatority property is proposed. Examples illustrating proposed results for Van der Pol system, Lorenz system, and Hindmarsh–Rose neuron model as well as computer simulation results are given

Changes in Neuropil Ultrastructure in Hippocampal Field CA1 in Rat Pups after Application of Hyaluronidase

Electron microscopy and electrophysiological studies were performed on cross-sectional slices of the hippocampus of four-week-old male rat pups (n = 35) to detect ultrastructural changes in hippocampal field CA1 and the characteristics of the formation of excitatory postsynaptic potentials in this area of the brain after incubation of slices in hyaluronidase solution (10 U/ml), whose specific substrate is the extracellular matrix glycosaminoglycan hyaluronic acid. At 1.5 min after enzyme application, there were reductions in synaptic cleft widths in axodendritic contacts of the striatum radiatum of hippocampal field CA1 by 15–25%, which were consistent with increases seen in the amplitudes of excitatory postsynaptic potentials. At 4.5 min of incubation, the lumens of synaptic clefts decreased by 45–55%: during this time there was blockade of signal transmission via Schäffer collaterals to hippocampal field CA1. Thus, the structural-functional state of glycosaminoglycans is among the factors determining the efficiency of synaptic transmission in the brain