Two oscillators having natural frequencies δ and γ and damping coefficients proportional to -λ are weakly coupled through cubic nonlinearities. As λ is increased through λc ≡ 0, nonlinear solutions of amplitude ɛ bifurcate. To leading order in ɛ such systems (including the case of coupled van der Pol oscillators) have behaviors governed by the single parameter ρ ∼ 2(δ-γ)/(λ-λc). ρ has a critical value ρc determined by a Josephson-junction equation. For |ρ| > ρ the oscillations are quasiperiodic; the modulations die out in the far-from-resonance case |ρ| → ∞. For |ρ| < ρ there are phase-locked oscillations and competing stable states can occur. An increase in λ, causing |ρ| to cross ρ, results in a type of reverse bifurcation (quasiperiodic to periodic). No chaotic behavior is found.
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