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We propose to compute the effective activation energy, usually referred to a pseudopotential or quasipotential, of a birhythmic system -- a van der Pol like oscillator -- in the presence of correlated noise. It is demonstrated, with analytical techniques and numerical simulations, that the correlated noise can be taken into account and one can retrieve the low noise rate of the escapes. We thus conclude that a pseudopotential, or an effective activation energy, is a realistic description for the stability of birhythmic attractors also in the presence of correlated noise.
We investigate the effects of exponentially correlated noise on birhythmic van der Pol type oscillators. The analytical results are obtained applying the quasi-harmonic assumption to the Langevin equation to derive an approximated Fokker-Planck equat
We find exact mappings for a class of limit cycle systems with noise onto quasi-symplectic dynamics, including a van der Pol type oscillator. A dual role potential function is obtained as a component of the quasi-symplectic dynamics. Based on a stoch
The analysis of a birhythmic modified van der Pol type oscillator driven by periodic excitation and L`evy noise shows the possible occurrence of coherence resonance and stochastic resonance. The frequency of the harmonic excitation in the neighborhoo
The equation of the Van der Pol oscillator, being characterized by a dissipative term, is non-Lagrangian. Appending an additional degree of freedom we bring the equation in the frame of action principle and thus introduce a one-way coupled system. As
Classical dynamical systems close to a critical point are known to act as efficient sensors due to a strongly nonlinear response. We explore such systems in the quantum regime by modeling a quantum version of a driven van der Pol oscillator. We find