A new model of a controlled neuron oscillator, proposed earlier {Kryukov et al, 1986} for the interpretation of the neural activity in various parts of the central nervous system, may have important applications in engineering and in the theory of brain functions. The oscillator has a good stability of the oscillation period, its frequency is regulated linearly in a wide range and it can exhibit arbitrarily long oscillation periods without changing the time constants of its elements. The latter is achieved by using the critical slowdown in the dynamics arising in a network of nonformal excitatory neurons {Kovalenko et al, 1984, Kryukov, 1984}. By changing the parameters of the oscillator one can obtain various functional modes which are necessary to develop a model of higher brain function.