Generic bifurcation structures of Arnol’d tongues in forced oscillators

Generic bifurcation structures of Arnol'd tongues in forced oscillators.

Lighting Arnold Flames: Resonance in Doubly Forced Periodic Oscillators

We study doubly forced nonlinear planar oscillators: ẋ = V(x) + α1W1(x, ω1t) + α2W2(x, ω2t), whose forcing frequencies have a fixed rational ratio: ω1 = m n ω2. After some changes of parameter, we arrive at the form we study: ẋ = V(x) + α{(2 − γ)W1(x, m ω0 β t) + (γ − 1)W2(x, n ω0 β t)}. We assume ẋ = V(x) has an attracting limit cycle — the unforced planar oscillator — with frequency ω0, and t...

Scaling of the Arnold tongues

When two oscillators are coupled together there are parameter regions called ‘Arnold tongues’ where they mode lock and their motion is periodic with a common frequency. We perform several numerical experiments on a circle map, studying the width of the Arnold tongues as a function of the period q , winding number p / q , and nonlinearity parameter k , in the subcritical region below the transit...

Arnold tongues in human cardiorespiratory systems.

Arnold tongues are phase-locking regions in parameter space, originally studied in circle-map models of cardiac arrhythmias. They show where a periodic system responds by synchronizing to an external stimulus. Clinical studies of resting or anesthetized patients exhibit synchronization between heart-beats and respiration. Here we show that these results are successfully modeled by a circle-map,...

Mode locking and Arnold tongues in integrate-and-fire neural oscillators.

An analysis of mode-locked solutions that may arise in periodically forced integrate-and-fire (IF) neural oscillators is introduced based upon a firing map formulation of the dynamics. A q:p mode-locked solution is identified with a spike train in which p firing events occur in a period qDelta, where Delta is the forcing period. A linear stability analysis of the map of firing times around such...