This paper studies an integrate-and-fire circuit with a periodic input. It has two states and has rich dynamics: as a DC input varies, it can exhibit period doubling bifurcation to chaos; as a periodic input is applied, the periodic or chaotic phenomenon (for a DC input) is changed into interesting synchronous or asynchronous phenomenon. Using a mapping procedure, we can elucidate parameter subspace in which the synchronous phenomena occur. Using a test circuit, typical phenomena can be verified in the laboratory.

An electrophysiological experiment showed that spike timing was precise to less than one millisecond. This result indicates the possibility in the precise time codings. For a high accurate time coding, reconsideration of a neural mechanism which decides firing time is required. From such viewpoint, we quantitatively examined change in firing time with interference between two synaptic inputs through Hodgkin-Huxley (HH) and integrate-and-fire (IF) model neurons. The precise firing times in the HH model neuron were extremely different from those in the IF model neuron. In this paper, the relations of input intensity to firing time are investigated in the other more two pulse generation models: Morris-Lecar (ML) and FitzHugh-Nagumo (FN) model. The result of the ML model in a certain parameter set (type-I) exhibited monotone decreasing like that of the IF model while the result of the ML model in the otter parameter set (type-II) exhibited non-monotone decreasing like that of the HH model. The result of the FN model exhibited non-monotone decreasing like the HH model despite its qualitativeness. Next the firing patterns in the four model neurons on a model of V1 (primary visual area) and LGN (lateral geniculate nucleus) with circular and mutual excitatory connections are investigated to show how dependent on model neurons the firing patterns are. The spikes in the HH, the ML type-II, and the FN model neurons elicited synchronous oscillations while the spikes in the IF and the ML type-I model neurons did not; the firing patterns dramatically changed with the dependence on the model neurons.

This paper studies mutually coupled integrate-and-fire type chaotic oscillators. The coupling is realized by impulsive switchings and the system exhibits various synchronous and asynchronous phenomena. We give a basic classification of the chaos synchronization phenomena and their breakdown patterns. The stability of the synchronous states can be confirmed using the piecewise exact solutions, and the basic mechanism of the phenomena can be elucidated by a simple geometric consideration. The typical phenomena are confirmed in the laboratory.

In this paper, we consider the Integrate-and-Fire Model (ab. IFM) with two periodic inputs. The IFM outputs a pulse-train which is governed by a one dimensional return map. Using the return map, the relationship between the inputs and the output is clarified: the first input determines the global shape of the return map and the IFM outputs various periodic and chaotic pulse-trains; the second input quantizes the state of the return map and the IFM outputs various periodic pulse-trains. Using a computer aided analysis method, the quantized return map can be analyzed rigorously. Also, some typical phenomena are confirmed in the laboratory.