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Register a new userCan L`evy noise induce coherence and stochastic resonances in a birhythmic van der Pol system?
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Added by
Giovanni Filatrella
Publication date
2021
fields
Physics
and research's language is
English
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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 neighborhood of one of the limit cycles influences the coherence of the dynamics on the time scale of intrawell oscillations. The autocorrelation function, the power spectral density and the signal-to-noise-ratio used in this analysis are shown to be maximized for an appropriate choice of the noise intensity. A proper adjustment of the L`evy noise intensity enhances the output power spectrum of the system, that is, promotes stochastic resonance. Thus, the robustness of the resonance, that seems to occur also in the presence of nonstandard noise, is examined using standard measures. The initial selection of the attractor seems to have an influence on the coherence, while the skewness parameter of the L`evy noise has not a notable impact on the resonant effect.
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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 equation. This approach allows to analytically derive the probability distributions as well as the activation energies associated to switching between coexisting attractors. The stationary probability density function of the van der Pol oscillator reveals the influence of the correlation time on the dynamics. Stochastic bifurcations are discussed through a qualitative change of the stationary probability distribution, which indicates that noise intensity and correlation time can be treated as bifurcation parameters. Comparing the analytical and numerical results, we find good agreement both when the frequencies of the attractors are about equal or when they are markedly different.
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.
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 with the Van der Pol oscillator, the coupled system also involves only one parameter that controls the dynamics. The response system is described by a linear differential equation coupled nonlinearly to the drive system. In the linear approximation the equations of our coupled system coincide with those of the Bateman dual system (a pair of damped and anti-damped harmonic oscillators). The critical point of damped and anti-damped oscillators are stable and unstable for all physical values of the frictional coefficient $mu$. Contrarily, the critical points of the drive- (Van der Pol) and response systems depend crucially on the values of $mu$. These points are unstable for $mu > 0$ while the critical point of the drive system is stable and that of the response system is unstable for $mu < 0$. The one-way coupled system exhibits bifurcations which are different from those of the uncoupled Van der Pol oscillator. Our system is chaotic and we observe phase synchronization in the regime of dynamic chaos only for small values of $mu$.
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 the classical response survives down to one excitation quantum. At very weak drives, genuine quantum features arise, including diverging and negative susceptibilities. Further, the linear response is greatly enhanced by using a strong incoherent pump. These results are largely generic and can be probed in current experimental platforms suited for quantum sensing.
The objective of this paper is to explore the possibility to couple two van der Pol (vdP) oscillators via a resistance-capacitance (RC) network comprising a Ag-TiOx-Al memristive device. The coupling was mediated by connecting the gate terminals of two programmable unijunction transistors (PUTs) through the network. In the high resistance state (HRS) the memresistance was in the order of MOhm leading to two independent selfsustained oscillators characterized by the different frequencies f1 and f2 and no phase relation between the oscillations. After a few cycles and in dependency of the mediated pulse amplitude the memristive device switched to the low resistance state (LRS) and a frequency adaptation and phase locking was observed. The experimental results are underlined by theoretically considering a system of two coupled vdP equations. The presented neuromorphic circuitry conveys two essentials principle of interacting neuronal ensembles: synchronization and memory. The experiment may path the way to larger neuromorphic networks in which the coupling parameters can vary in time and strength and are realized by memristive devices.
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