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Register a new userSynchronization of two memristive coupled van der Pol oscillators
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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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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.
Time-periodic perturbations of an asymmetric Duffing-Van-der-Pol equation close to an integrable equation with a homoclinic figure-eight of a saddle are considered. The behavior of solutions outside the neighborhood of figure-eight is studied analytically. The problem of limit cycles for an autonomous equation is solved and resonance zones for a nonautonomous equation are analyzed. The behavior of the separatrices of a fixed saddle point of the Poincare map in the small neighborhood of the unperturbed figure-eight is ascertained. The results obtained are illustrated by numerical computations.
Neural coupled oscillators are a useful building block in numerous models and applications. They were analyzed extensively in theoretical studies and more recently, in biologically realistic simulations of spiking neural networks. The advent of mixed-signal analog/digital neuromorphic electronic circuits provides new means for implementing neural coupled oscillators on compact low-power spiking neural network hardware platforms. However, their implementation on this noisy, low-precision and inhomogeneous computing substrate raises new challenges with regards to stability and controllability. In this work, we present a robust, spiking neural network model of neural coupled oscillators and validate it with an implementation on a mixed-signal neuromorphic processor. We demonstrate its robustness showing how to reliably control and modulate the oscillators frequency and phase shift, despite the variability of the silicon synapse and neuron properties. We show how this ultra-low power neural processing system can be used to build an adaptive cardiac pacemaker modulating the heart rate with respect to the respiration phases and compare it with surface ECG and respiratory signal recordings of dogs at rest. The implementation of our model in neuromorphic electronic hardware shows its robustness on a highly variable substrate and extends the toolbox for applications requiring rhythmic outputs such as pacemakers.
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.
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