The paper presents an information model for representation of brain linear and nonlinear resonance phenomena based on information nullors. In the brain functions the rhythms and quasi periodicity of processes in neural networks play the outstanding (significant) role. It is why adaptive resonance theory (ART) including resonant effects has been studied for a long time by many authors. The periodicity in the transfers of signals between the long-term memory (LTM) and short-term memory (STM) creates a possibility of resonance system structure. LTM with information content representing expectations and STM covering sensory information in resonance process offer effective learning. Nonlinear adaptive resonance creates conditions for new knowledge, or inventory observation. In the paper this feature is newly modelled by an information gyrator that best fits these linear and non-linear phenomena.