Optimal Phase-Control Strategy for Damped-Driven Duffing Oscillators.

Phase-control techniques of chaos aim to extract periodic behaviors from chaotic systems by applying weak harmonic perturbations with a suitably chosen phase. However, little is known about the best strategy for selecting adequate perturbations to reach desired states. Here we use experimental measures and numerical simulations to assess the benefits of controlling individually the three terms of a Duffing oscillator. Using a real-time analog indicator able to discriminate on-the-fly periodic behaviors from chaos, we reconstruct experimentally the phase versus perturbation strength stability areas when periodic perturbations are applied to different terms governing the oscillator. We verify the system to be more sensitive to perturbations applied to the quadratic term of the double-well Duffing oscillator and to the quartic term of the single-well Duffing oscillator.

Chaotic dynamics of a magnetic nanoparticle.

We study the deterministic spin dynamics of an anisotropic magnetic particle in the presence of a magnetic field with a constant longitudinal and a time-dependent transverse component using the Landau-Lifshitz-Gilbert equation. We characterize the dynamical behavior of the system through calculation of the Lyapunov exponents, Poincaré sections, bifurcation diagrams, and Fourier power spectra. In particular we explore the positivity of the largest Lyapunov exponent as a function of the magnitude and frequency of the applied magnetic field and its direction with respect to the main anisotropy axis of the magnetic particle. We find that the system presents multiple transitions between regular and chaotic behaviors. We show that the dynamical phases display a very complicated structure of intricately intermingled chaotic and regular phases.

Periodic neural activity induced by network complexity.

We study a model for neural activity on the small-world topology of Watts and Strogatz and on the scale-free topology of Barabási and Albert. We find that the topology of the network connections may spontaneously induce periodic neural activity, contrasting with nonperiodic neural activities exhibited by regular topologies. Periodic activity exists only for relatively small networks and occurs with higher probability when the rewiring probability is larger. The average length of the periods increases with the square root of the network size.