THE AUTONOMOUS CHAOTIC RELAXATION-OSCILLATOR - AN ELECTRICAL ANALOG TO THE DRIPPING FAUCET

Both experimental and theoretical techniques have been employed to study the dynamics of an electrical relaxation oscillator that stimulates internal resonances. This autonomous chaotic relaxation oscillator (ACRO) circuit reproduces the type of aperiodic behavior that may be found in many physical systems such as dripping faucets, magnetospheric substorms, bowed musical instruments, or frictional brakes. The ACRO circuit displays a wide range of intermittency as the average pulse period and the internal damping rates are varied. Small changes in circuit parameters can produce sudden, hysteretic transitions from stable to quasiperiodic or aperiodic outputs. Using pulse period spectra, first return maps, Poincare sections, projections of trajectories, Lyapunov exponents, and power spectra, the full range of ACRO behavior is characterized.