Memory and forgetting processes with the firing neuron model

The aim of this paper is to present a novel algorithm for learning and forgetting within a very simplified, biologically derived model of the neuron, called firing cell (FC). FC includes the properties: (a) delay and decay of postsynaptic potentials, (b) modification of internal weights due to propagation of postsynaptic potentials through the dendrite, (c) modification of properties of the analog weight memory for each input due to a pattern of long-term synaptic potentiation. The FC model could be used in one of the three forms: excitatory, inhibitory, or receptory (ganglion cell). The computer simulations showed that FC precisely performs the time integration and coincidence detection for incoming spike trains on all inputs. Any modification of the initial values (internal parameters) or inputs patterns caused the following changes of the interspike intervals time series on the output, even for the 10 s or 20 s real time course simulations. It is the basic evidence that the FC model has chaotic dynamical properties. The second goal is the presentation of various nonlinear methods for analysis of a biological time series.