ODE's ode Pablo Riera Laboratorio de Inteligencia Artificial - - PowerPoint PPT Presentation

ODE's ode

Pablo Riera

Laboratorio de Inteligencia Artificial Aplicada, Instituto de Ciencias de la Computación, Universidad de Buenos Aires, CONICET, Argentina

4th Febraury, IMPA, Rio de Janeiro

Overview

• Background
• Dinamical Systems

○ ODEs, Maps ○ Vector fields, phase portrait ○ Non linear systems, bifurcations, chaos

• Playing with ODEs
• Live ODEing with LODE

○ Yaml interface

• Sound synthesis with ODEs

○ Supercollider Plugin ○ C++ shared libraries

• Demo

Background

• Generative music with spiking neural

networks and EEG

Dynamical Systems

• Systems that describe the time dependence of a point in a space with a

function

• Typical systems:

○ Continuous: Ordinary Differential Equations (ODE) ○ Discrete: Difference Equations (Maps)

Dynamical Systems

• Vector fields
• Phase Portrait

http://kevbase.com/phase/

Example: simple harmonic oscillator

Dynamical Systems

• Iterated Maps
• Bifurcations

Example: Logistic Map

Playing with ODEs

• Temporal scale
• Chaos
• Noise
• External Inputs
• Delay

Live ODEing with LODE

Sound Synthesis with ODEs

• Numerical solutions of ODEs with Runge Kutta 4 method
• New Supercollider Extension Plugins

○ Oderk4 ○ Odemap

• Dynamic loading of shared libraries of equation definitions

Sound Synthesis with ODEs