Phenomenology of coupled nonlinear oscillators

Abstract

A recently introduced model of coupled nonlinear oscillators in a ring is revisited in terms of its information processing capabilities. The use of Lempel-Ziv based entropic measures allows to study thoroughly the complex patterns appearing in the system for different values of the control parameters. Such behaviors, resembling cellular automata, have been characterized both spatially and temporally. Information distance is used to study the stability of the system to perturbations in the initial conditions and in the control parameters. The latter is not an issue in cellular automata theory, where the rules form a numerable set, contrary to the continuous nature of the parameter space in the system studied in this contribution. The variation in the density of the digits, as a function of time is also studied. Local transitions in the control parameter space are also discussed.

Computational capabilities at the edge of chaos for one dimensional systems undergoing continuous transitions

“…The system exhibits, for certain ranges of values of its control parameters, complex behavior. The local nature of the coupling, where the phase of one oscillator is directly related to two other neighbors, and the rich set of behaviors resembles that of the phenomena found in CA 36 . The array of coupled oscillators obeys, for the phase evolution, a system of equations given by…”

“…A detailed study of the "phase" diagram has been done before ( Figure 3 shows the phase diagram taken from Ref. 36). There are several particular regions in the control parameter space.…”

“…and is insensitive to perturbations in the initial configuration of the oscillators, while the surrounding chaotic region has high entropy rate and high d LZ values (See figures 3 and 7 in Estevez et al 36 ). We chose a fixed γ value of 1.2057 and let ω vary between 2.10 and 2.54, enough to make a transition from the needle region to the chaotic region.…”

Nonlinear dynamics and energy transfer for two rotating dipoles in an external field: A complete dimensional analysis

“…For a given orbit with initial conditions r(0) and δr(0), the numerical integration of equations (20) and (21)…”

“…The mechanism of energy transport mediated by the dipole-dipole interaction is closely related to the nonlinear behavior of many-body systems and has attracted special attention in classical dynamics [15][16][17][18][19][20]. Most of the nonlinear dynamical studies on coupled rotating dipoles restrict their motion to planar rotations.…”