"A Coupled Oscillator Model for Emergent Cognitive Process"
Numerous papers have been published concerning mathematical models of memory and learning of human brain activity. However, research proposing mathematical models for the creative cognition process such as intuition for linkage to creativity has seldom been conducted. In this paper for a description of the emergent cognitive process, the author proposes a new Lorenz model with two parameters, temporal coefficient c and spatial coefficient d. This spatiotemporal coupled Lorenz model is a device that has coupled three 1-dimensional information codes. This device can be used as an emergent device for three channels through control of on-off intermittent chaos as observed in this model with the c and d as parameters. The c and d control on-off intermittent chaos, although they have no direct effect on individual vectors, the c and d work as independent parameters without providing internal disturbance. The wandering on the three 1-dimensional information coded space in the burst phase with seeking and gathering of valuable information from this, synchronized stabilization on a point in the laminar phase can be modeled as a process that intermittently and irregularly repeats. For instance, this is a motivation of the research, when one hears a musical work, one is listening while perceiving mainly the elements comprising the musical work, one is listening the textures that these numerous elements weave. The subject of music perception and cognition is often experienced as a rapid and irregular change with time. (Note: Using an example of a visually perceived phenomenon, the cognitive process is where the figure and background change rapidly and irregularly in turns like Rubin’s vase or Necker cube. The proposed model may concern coincidence detector, e.g., Gray & Singer , Koenig & Schilen , Varela et al .) Then, analyzing the musical work’s structures of Beethoven, Brahms, Wagner, for example, like Masterpieces, a melody is present here, although the melody and harmony are inseparable; there is absolutely no way to first have the melody and then harmonization with it. Moreover, the melody and harmony are allocated to individual instruments such as woodwinds, brasses and strings for respective sounds and with harmonic progression are changed to be extremely effective as melody; if melody and harmony do not exist simultaneously and if changes in both harmonic progression and timbre in the process of creation do not exist simultaneously in the brain of the composer as a sound image, then creation of a work like this would be close to impossible. That is, harmony, melody, and timbre are in a mode where they are blended into one another and creation must be interpreted to progress with simultaneous processing of these in parallel in the brain of the composer. However, the music theory proposed until now is only static system theory, e.g., GTTM [Lerdahl & Jackendoff, 1983], PCST [Forte, 1973], and dynamic system theory do not exist yet. In this presentation, the author discusses about proposed paper and mentions also a work: Emura , "Les Papillons de Lorenz", Editions Billaudot, Paris.