Abstract
We consider the response to uncorrelated noise and harmonic excitation of a birhythmic van der Pol-type oscillator. This system, as opposed to the standard van der Pol oscillator, is characterized by two stable orbits. The noisy oscillator can be analytically mapped, with the technique of stochastic averaging, onto an ordinary bistable system with a bistable (quasi)potential. The birhythmic oscillator can also be numerically characterized through the diagnostics of coherent resonance and the signal-to-noise-ratio. The analysis shows the presence of noise-induced coherent states, influenced by the different time scales of the oscillator.
Highlights
We propose to add a sinusoidal drive to such effective bistable potential, i.e. we consider a forced van der Pol type birhythmic system [34] as in some biological systems that are characterized by a forcing term [35]
We propose to extend the same diagnostic used by Pikovski and Kurths [49] to the stochastic birhythmic van der Pol model to detect the occurrence of Coherence Resonance (CR)
We have investigated the effect of noise added to a forced birhythmic van der Pol-like system that describes some applications as, e.g., enzymatic reactions, sleep-awake cycles, and energy harvesting
Summary
We propose to add a sinusoidal drive to such effective bistable potential, i.e. we consider a forced van der Pol type birhythmic system [34] as in some biological systems that are characterized by a forcing term [35]. B (2017) 90: 153 drive can co-operate, producing states that are, in some statistical sense, coherent with the external drive This is the property exploited in Stochastic Resonance (SR) [36], stochastic signal detection [37,38], and dynamical phase transitions [39]. It is not obvious that SR can occur, and this is the objective of our research: to investigate if a birhythmic system, where the two states are periodic orbit with an intrinsic time scale, can exhibit a (stochastic) resonance in the presence of noise, as the analogous ordinary bistable systems.
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