Physics 256 Natural Computation & Self-Organization Coupled-Oscillator Models: State-Space & Dynamics

Objects and systems at all scales operate by a mix of internal impulsion and external influence. This phenomenon, ubiquitous and accurately modeled by simple systems of coupled oscillators, are observed in systems of elementary subatomic particle, biological populational dynamics and interactions of heavenly bodies on an astronomical scale. Despite the simplicity of coupled oscillator models like Kuramoto’s and the Dripping Handrail, they contain rich behavior such as phase transitions and harbor computational capabilities. The combination of simplicity, leading to mathematical tractability, and rich behavior is why coupled oscillator systems are so heavily studied. We study the dynamics and information storage capacity of a small, simple system of coupled oscillators with ultimate goals of elucidating neural oscillatory behavior and investigating the computational benefits that such oscillatory behavior might engender. We map out the phase space and dynamics of a single discrete-time, discrete space Dripping Handrail (DH) oscillator system and examine what additional complexities arise when two DH oscillators are coupled together. We investigate interactions between natural frequencies, coupling strengths, coherence, coupled frequencies and relative phase of a two oscillator system. We also discuss the application of these ideas to a 3 DH oscillator system and the additional considerations for systems of 3+ oscillators.