Autonomous Oscillations Research Articles

Experimental evidence of quint points and non-quantum chirality in a minimalist autonomous electronic oscillator

Recent intensive simulations have uncovered remarkable phenomena in stability diagrams of classical oscillators, for instance, quint points, parameter rings, and chiral structures of non-quantum origin. So far, their experimental observation has remained elusive. Here, using a simple electronic circuit, we report the experimental detection of five phases of oscillation spread around a quint point, an exceptional point where five oscillatory modes meet. This finding corroborates predictions of non-quantum chirality in the control parameter space of nonlinear oscillators governed by rate equations.

Optimization of a control law to synchronize first-order dynamical systems on Riemannian manifolds by a transverse component

<p style='text-indent:20px;'>The present paper builds on the previous contribution by the second author, S. Fiori, <i>Synchronization of first-order autonomous oscillators on Riemannian manifolds</i>, Discrete and Continuous Dynamical Systems – Series B, Vol. 24, No. 4, pp. 1725 – 1741, April 2019. The aim of the present paper is to optimize a previously-developed control law to achieve synchronization of first-order non-linear oscillators whose state evolves on a Riemannian manifold. The optimization of such control law has been achieved by introducing a transverse control field, which guarantees reduced control effort without affecting the synchronization speed of the oscillators. The developed non-linear control theory has been analyzed from a theoretical point of view as well as through a comprehensive series of numerical experiments.</p>

Mathematical Model of Satellite Rotation near Spin-Orbit Resonance 3:2

This paper considers the rotational motion of a satellite equipped with flexible viscoelastic rods in an elliptic orbit. The satellite is modeled as a symmetric rigid body with a pair of flexible viscoelastic rods rigidly attached to it along the axis of symmetry. A planar case is studied, i. e., it is assumed that the satellite’s center of mass moves in a Keplerian elliptic orbit lying in a stationary plane and the satellite’s axis of rotation is orthogonal to this plane. When the rods are not deformed, the satellite’s principal central moments of inertia are equal to each other. The linear bending theory for thin inextensible rods is used to describe the deformations. The functionals of elastic and dissipative forces are introduced according to this model. The asymptotic method of motions separation is used to derive the equations of rotational motion reflecting the influence of the fluctuations, caused by the deformations of the rods. The method of motion separation is based on the assumption that the period of the autonomous oscillations of a point belonging to the rod is much smaller than the characteristic time of these oscillations’ decay, which, in its turn, is much smaller than the characteristic time of the system’s motion as a whole. That is why only the oscillations induced by the external and inertial forces are taken into account when deriving the equations of the rotational motion. The perturbed equations are described by a third-order system of ordinary differential equations in the dimensionless variable equal to the ratio of the satellite’s absolute value of angular velocity to the mean motion of the satellite’s center of mass, the angle between the satellite’s axis of symmetry and a fixed axis and the mean anomaly. The right-hand sides of the equation depend on the mean anomaly implicitly through the true anomaly. A new slow angular variable is introduced in order to perform the averaging for the perturbed system near the 3:2 resonance, and the averaging is

Reaction-Diffusion Dynamics of pH Oscillators in Oscillatory Forced Open Spatial Reactors.

Studying the effect of coupling and forcing of oscillators is a significant area of interest within nonlinear dynamics and has provided evidence of many interesting phenomena, such as synchronization, beating, oscillatory death, and phase resetting. Many studies have also reported along this line in reaction–diffusion systems, which are preferably explored experimentally by using open reactors. These reactors consist of one or two homogeneous (well-stirred) tanks, which provide the boundary conditions for a spatially distributed part. The spatiotemporal dynamics of this configuration in the presence of temporal oscillations in the homogeneous part has not been systematically investigated. This paper aims to explore numerically the effect of time-periodic boundary conditions on the dynamics of open reactors provided by autonomous and forced oscillations in the well-stirred part. A simple model of pH oscillators can produce various phenomena under these conditions, for example, superposition and modulation of spatiotemporal oscillations and forced bursting. The autonomous oscillatory boundary conditions can be generated by the same kinetic instabilities that result in spatiotemporal oscillations in the spatially distributed part. The forced oscillations are induced by sinusoidal modulation on the inflow concentration of the activator in the tank. The simulations confirmed that this type of forcing is more effective when the modulation period is longer than the residence time of the well-stirred part. The use of time-periodic boundary conditions may open a new perspective in the control and design of spatiotemporal phenomena in open one-side-fed and two-side-fed reactors.

Light-dependent reactions of animal circadian photoreceptor cryptochrome.

Circadian rhythms are endogenous autonomous 24-h oscillations that are generated by a transcription-translation feedback loop (TTFL). In the positive arm of the TTFL, two transcription factors activate the expression of two genes of the negative arm as well as circadian clock-regulated genes. The circadian clocks are reset through photoreceptor proteins by sunlight in the early morning to keep synchrony with the geological clock. Among animal circadian photoreceptors, Drosophila Cryptochrome (DmCRY) has some unique properties because Drosophila has a single cryptochrome (CRY) that appears to have functions which are specific to organs or tissues, or even to a subset of cells. In mammals, CRYs are not photoreceptors but function in the TTFL, while insects have a light-insensitive mammalian-like CRY or a Drosophila-like photoreceptor CRY (or both). Here, we postulate that as being just one CRY in Drosophila, DmCRY might play different roles in different tissues/organs in a context-dependent manner. In addition to being a circadian photoreceptor/protein, attributing also a magnetoreception function to DmCRY has increased its workload. Considering that DmCRY senses photons as a photoreceptor but also can regulate many different events in a light-dependent manner, differential protein-protein interactions (PPIs) of DmCRY might play a critical role in the generation of such diverse outputs. Therefore, we need to add novel approaches in addition to the current ones to study multiple and context-dependent functions of DmCRY by adopting recently developed techniques. Successful identification of transient/fast PPIs on a scale of minutes would enhance our understanding of light-dependent and/or magnetoreception-associated reactions.

Systematic Studies of the Circadian Clock Genes Impact on Temperature Compensation and Cell Proliferation Using CRISPR Tools.

Simple SummaryOne of the major characteristics of the circadian clock is temperature compensation, and previous studies suggested a single clock gene may determine the temperature compensation. In this study, we report the first full collection of clock gene knockout cell lines using CRISPR/Cas9 tools. Our full collections indicate that the temperature compensation is a complex gene regulation system instead of being regulated by any single gene. Besides, we systematically compared the proliferation rates and circadian periods using our full collections, and we found that the cell growth rate is not dependent on the circadian period. Therefore, complex interaction between clock genes and their protein products may underlie the mechanism of temperature compensation, which needs further investigations.Mammalian circadian genes are capable of producing a self-sustained, autonomous oscillation whose period is around 24 h. One of the major characteristics of the circadian clock is temperature compensation. However, the mechanism underlying temperature compensation remains elusive. Previous studies indicate that a single clock gene may determine the temperature compensation in several model organisms. In order to understand the influence of each individual clock gene on the temperature compensation, twenty-three well-known mammalian clock genes plus Timeless and Myc genes were knocked out individually, using a powerful gene-editing tool, CRISPR/Cas9. First, Bmal1, Cry1, and Cry2 were knocked out as examples to verify that deleting genes by CRISPR is effective and precise. Cell lines targeting twenty-two genes were successfully edited in mouse fibroblast NIH3T3 cells, and off-target analysis indicated these genes were correctly knocked out. Through measuring the luciferase reporters, the circadian periods of each cell line were recorded under two different temperatures, 32.5 °C and 37 °C. The temperature compensation coefficient Q10 was subsequently calculated for each cell line. Estimations of the Q10 of these cell lines showed that none of the individual cell lines can adversely affect the temperature compensation. Cells with a longer period at lower temperature tend to have a shorter period at higher temperature, while cells with a shorter period at lower temperature tend to be longer at higher temperature. Thus, the temperature compensation is a fundamental property to keep cellular homeostasis. We further conclude that the temperature compensation is a complex gene regulation system instead of being regulated by any single gene. We also estimated the proliferation rates of these cell lines. After systematically comparing the proliferation rates and circadian periods, we found that the cell growth rate is not dependent on the circadian period.

Circadian Oscillation of Natural Antisense Transcripts Related to Human Core Clock Genes

Circadian clocks are autonomous intracellular oscillators that synchronize metabolic and physiological processes with the external signals. So, misalignment of environmental and endogenous circadian rhythms leads to disruption of biological activities in living organisms. Noncoding transcripts including antisense RNAs are an important component of the molecular clocks. Commonly, the antisense transcripts are involved in the regulation of gene expression. PER2AS and CRY1AS are the only known Natural Antisense Transcripts (NAT) among the core clock genes, which overlap with the PER2 and CRY1 genes, respectively. In this study, we hypothesized that PER2AS and CRY1AS like the other clock genes, exhibit the oscillatory behavior in a 24-hour period and affect the expression of PER2 and CRY1. First, the A549 cell line was cultured under standard conditions. After horse serum shock, RNA extraction and cDNA synthesis was performed; then the expression fluctuations of PER2AS, CRY1AS, PER2, and CRY1 were measured with Real-time PCR. Our result showed that PER2AS and CRY1AS had similar oscillation patterns with their sense strand during 24-hour period. Therefore, we suggested that PER2AS and CRY1AS transcripts probably by preventing the interaction of miRNAs with PER2 and CRY1 mRNAs, influence the expression of them, positively.

Identification of van der Pol oscillator network parameters

The problem of state observation and parameters identification of an oscillatory system consisting of coupled van der Pol oscillators is considered. The unknowns are: velocity of oscillations and parameters that characterize the threshold values for displacements of network's oscillators at which the damping forces change sign. An invariant relations method for simultaneous of the state and parameters estimation is used. Such approach is based on dynamical extension of original system and synthesis of appropriate invariant relations, from which the unknowns can be expressed as a function of the known quantities on the trajectories of extended system during the observed motion. The stability property is formally checked considering the oscillatory behavior of the system. On the first step the corresponding observation and identification problems are solved for one of autonomous van der Pol oscillator, further, the results obtained are extended to a system of interconnected oscillators. The simulation results confirm efficiency of the proposed scheme of nonlinear observer and identifier design for network of oscillators.

Chirality detected in Hartley\u2019s electronic oscillator

Chirality is an elusive asymmetry important in science and technology and confined mainly to the quantum realm. This paper reports the observation of chirality in a classical (that is, not quantum) scenario, namely in stability diagrams of an autonomous electronic oscillator with a junction-gate field-effect transistor (JFET) and a tapped coil. As the number of spikes (local maxima) of stable oscillations changes along closed parameter paths, they generate two types of intricate structures. Surprisingly, such pair of structures are artful images of each other when reflected on a mirror. They are dual chiral pairs interconnecting families of stable oscillations in closed loops. Chiral pairs should not be difficult to detect experimentally. This chirality is conjectured to be a generic property of nonlinear oscillators governed by classical (that is, not quantum) equations.

Moisture-induced autonomous surface potential oscillations for energy harvesting

A variety of autonomous oscillations in nature such as heartbeats and some biochemical reactions have been widely studied and utilized for applications in the fields of bioscience and engineering. Here, we report a unique phenomenon of moisture-induced electrical potential oscillations on polymers, poly([2-(methacryloyloxy)ethyl] dimethyl-(3-sulfopropyl) ammonium hydroxide-co-acrylic acid), during the diffusion of water molecules. Chemical reactions are modeled by kinetic simulations while system dynamic equations and the stability matrix are analyzed to show the chaotic nature of the system which oscillates with hidden attractors to induce the autonomous surface potential oscillation. Using moisture in the ambient environment as the activation source, this self-excited chemoelectrical reaction could have broad influences and usages in surface-reaction based devices and systems. As a proof-of-concept demonstration, an energy harvester is constructed and achieved the continuous energy production for more than 15,000 seconds with an energy density of 16.8 mJ/cm2. A 2-Volts output voltage has been produced to power a liquid crystal display toward practical applications with five energy harvesters connected in series.

Control of chaotic behavior in the dynamics of generalized Bonhoeffer-van der Pol system: Effect of asymmetric parameter

The effect of the asymmetric parameter in the dynamics, both of the forced Duffing van der Pol (DVdP) system and of the forced generalized Bonhoeffer-van der Pol (BVdP) system is investigated, namely the possibility for these systems to execute dynamics chaos even for large values of this asymmetric parameter. We have shown that the dynamics of the associated non dissipative and unforced system can be interpreted by means of an effective energy potential which may exhibit a two-hump or a two-well configuration according to the magnitude of the parameters of the system. In the two-well configuration, a pair of pulses of different amplitudes describing homoclinic orbits useful in the prediction of irregular dynamics for the associated forced system are analytically derived as well as the expression of the single pulse describing the single homoclinic orbit in the case of two-hump configuration and which leads to a kink-antikink pair (heteroclinic orbits) in the absence of the asymmetric parameter. By means of the Melnikov theory, the conditions for the existence of the transverse intersection of stable and unstable orbits or dynamics chaos are also derived. In the particular case for which the system can exhibit a pair of homoclinic orbits, the presence of the asymmetric parameter induces two types of domains among which a more favorable domain for the existence of chaotic behavior. In both cases, the asymmetric parameter reduces the domain range in which the system can execute regular dynamics and consequently increases its domain of a possible dynamics chaos. The accuracy of these analytical results is checked through the bifurcation diagrams and the corresponding Lyapunov exponents resulting from numerical simulations. It appears that the background properties of the unforced system, namely its capacity to exhibit autonomous oscillations and the stability of its equilibrium points which are closely connected to the magnitude of the asymmetric parameter, influence the accuracy of the analytical predictions.

Chimera states and frequency clustering in systems of coupled inner-ear hair cells.

Coupled hair cells of the auditory and vestibular systems perform the crucial task of converting the energy of sound waves and ground-borne vibrations into ionic currents. We mechanically couple groups of living, active hair cells with artificial membranes, thus mimicking in vitro the coupled dynamical system. We identify chimera states and frequency clustering in the dynamics of these coupled nonlinear, autonomous oscillators. We find that these dynamical states can be reproduced by our numerical model with heterogeneity of the parameters. Furthermore, we find that this model is most sensitive to external signals when poised at the onset of synchronization, where chimera and cluster states are likely to form. We, therefore, propose that the partial synchronization in our experimental system is a manifestation of a system poised at the verge of synchronization with optimal sensitivity.

The Efficiency of the Electro-Oxidation of Small Organic Molecules: Oscillations and Mechanism

Many hydrogen-carriers have been considered for the direct use in fuel cells and also in the electrochemical reform, where they are oxidized instead of water at lower potentials. We have investigated the electro-oxidation of formaldehyde, formic acid, methanol, and ethanol,[1] and of ethylene glycol, glycerol, and glucose[2] on polycrystalline platinum in acidic media, and compare the activity under conventional and oscillatory regimes. The comparison is carried out by different means and generalized by the use of simple identical experimental conditions in all cases. The activity along slow potentiodynamic curves, inferred by the peak current, decreases in the following sequence: formaldehyde ~ formic acid > methanol > ethanol ~ ethylene glycol > glucose > glycerol. The ubiquitous occurrence of potential oscillations under galvanostatic regime is associated with excursions of the electrode potentials to lower values, which noticeably decreases the overpotential of the anodic reaction, when compared to that in the absence of oscillations. Considerable enhancement in the power density was observed in an idealized fuel cell operated with those fuels when operated under oscillatory regime. Furthermore, the spontaneous periodic self-cleaning processes, present important advantages to the use of autonomous oscillations to reach both higher and long-term activities, and stability [3]. The discussion of these half-cell studies is complemented with experiments with proton exchange membrane fuel cells, namely direct liquid fuel cells (DLFCs). We have investigated the effect of temperature on DLFCs under conventional and oscillatory conditions.[4] Methanol, formic acid, ethanol, and dimethyl ether (DME) were used as fuels and identical experimental conditions were used in all cases. Some findings observed in half-cells are also observed in the DLFCs studied, but few peculiarities of the experimental configuration adopted in the later arise. Finally, mechanistic aspects underlying the observed dynamics are discussed.[1] M. V. F. Delmonde, L. F. Sallum, N. Perini, E. R. Gonzalez, R. Schlögl, H. Varela, J. Phys. Chem. C 120 (2016) 22365.[2] G. B. Melle, T. A. Ferreira, R. L. Romano, H. Varela, in preparation (2020).[3] J. A. Nogueira, P. P. Lopes, N. M. Markovic, H. Varela, Electrochem. Commun. 121 (2020) 106853.[4] J.A. Nogueira, H. Varela, Energy Fuels 34 (2020) 12995.

583 Hair cycle regulation by a mitochondrially localized protein: Is MPZL3 a central component of the elusive hair cycle clock?

Hair follicles (HFs) undergo cycles of growth (anagen), regression (catagen) and relative quiescence (telogen). The intrinsic and autonomous molecular oscillator system that drives the hair cycle (HC)—the “hair cycle clock (HCC)”—remains incompletely understood. In this study, we present evidence that Myelin Protein Zero-like 3 (MPZL3), a multifunctional nuclear-encoded protein localized in mitochondria and is primarily known to be involved in epidermal differentiation, also regulates the murine HCC. In the absence of functional MPZL3, Mpzl3 global knockout mice commence HF cycling with retarded first catagen-telogen transition after normal postnatal HF morphogenesis. However, they then display strikingly accelerated HF cycling, i.e., a precocious telogen-anagen transition during the second HC, compared to controls, suggesting that MPZL3 normally functions as an inhibitor of anagen entry. We also show that intrafollicular MPZL3 protein expression oscillates in an HC-dependent manner. In telogen HFs, MPZL3 is localized to the secondary hair germ, an epicenter of HC regulation, partially co-localizing with P-cadherin, in contrast to the hair matrix localization during early-mid anagen. Intriguingly, keratin 14 promoter-driven Cre-mediated Mpzl3 knockout mice recapitulate the precocious telogen-anagen transition during the second HC observed in global Mpzl3 knockout mice, indicating that skin epithelia-derived, MPZL3-dependent signals dictate the HCC. These findings introduce the novel concepts that a) mitochondria are more actively involved in HC control than previously recognized in the context of energy metabolism, b) MPZL3 plays a central role in the elusive HCC, and c) targeting MPZL3 and/or its downstream effectors may constitute an innovative and effective strategy for therapeutic HC manipulation in alopecia treatment.

Oscillatory Neural Networks Using VO2 Based Phase Encoded Logic.

Nano-oscillators based on phase-transition materials are being explored for the implementation of different non-conventional computing paradigms. In particular, vanadium dioxide (VO2) devices are used to design autonomous non-linear oscillators from which oscillatory neural networks (ONNs) can be developed. In this work, we propose a new architecture for ONNs in which sub-harmonic injection locking (SHIL) is exploited to ensure that the phase information encoded in each neuron can only take two values. In this sense, the implementation of ONNs from neurons that inherently encode information with two-phase values has advantages in terms of robustness and tolerance to variability present in VO2 devices. Unlike conventional interconnection schemes, in which the sign of the weights is coded in the value of the resistances, in our proposal the negative (positive) weights are coded using static inverting (non-inverting) logic at the output of the oscillator. The operation of the proposed architecture is shown for pattern recognition applications.

Autonomous Nanoscale Chemomechanical Oscillation on the Self-Oscillating Polymer Brush Surface by Precise Control of Graft Density.

As a novel functional surface, a self-oscillating polymer brush that undergoes autonomous, periodic swelling/deswelling during the Belousov-Zhabotinsky (BZ) reaction has been developed. Although extensive research has revealed how the fundamental aspects of the BZ reaction can be regulated based on the surface design of the self-oscillating polymer brush, design strategies for the induction of mechanical oscillation remain unexplored. Herein, we investigated the graft density effects on the phase transition behavior, which is an important design parameter for the mechanical oscillation of the modified polymer. The self-oscillating polymer-modified substrates with controlled graft densities were prepared by immobilizing various compositions of an initiator and a noninitiator followed by surface-initiated atom transfer radical polymerization of the self-oscillating polymer chains. In addition to the characterization of each prepared substrate, atomic force microscopy (AFM) and digital holographic microscopy (DHM) were employed to evaluate the density effects on the static and dynamic surface structures. AFM revealed that equilibrium swelling as well as thermoresponsive behavior is profoundly affected by the graft density. Moreover, using DHM, autonomous mechanical oscillation was captured only on the self-oscillating polymer brush with adequate graft density. Notably, the oscillation amplitude (150 nm) and the period (20 s) in this study were superior to those in a previous report on the self-oscillating polymer modified through the grafting-to method by 10- and 3-fold, respectively. This study presents design guidelines for future applications, such as autonomous transport devices.

Analysis, circuit realization and controls of an autonomous Morse jerk oscillator

Analysis, circuit realization and controls of an autonomous Morse jerk oscillator

A new approach on the modelling, chaos control and synchronization of a fractional biological oscillator

This research aims to discuss and control the chaotic behaviour of an autonomous fractional biological oscillator. Indeed, the concept of fractional calculus is used to include memory in the modelling formulation. In addition, we take into account a new auxiliary parameter in order to keep away from dimensional mismatching. Further, we explore the chaotic attractors of the considered model through its corresponding phase-portraits. Additionally, the stability and equilibrium point of the system are studied and investigated. Next, we design a feedback control scheme for the purpose of chaos control and stabilization. Afterwards, we introduce an efficient active control method to achieve synchronization between two chaotic fractional biological oscillators. The efficiency of the proposed stabilizing and synchronizing controllers is verified via theoretical analysis as well as simulations and numerical experiments.

Synchronization of oscillators with hyperbolic chaotic phases

Synchronization in a population of oscillators with hyperbolic chaotic phases is studied for two models. One is based on the Kuramoto dynamics of the phase oscillators and on the Bernoulli map applied to these phases. This system possesses an Ott-Antonsen invariant manifold, allowing for a derivation of a map for the evolution of the complex order parameter. Beyond a critical coupling strength, this model demonstrates bistability synchrony-disorder. Another model is based on the coupled autonomous oscillators with hyperbolic chaotic strange attractors of Smale-Williams type. Here a disordered asynchronous state at small coupling strengths, and a completely synchronous state at large couplings are observed. Intermediate regimes are characterized by different levels of complexity of the global order parameter dynamics.

Synchronization scenarios induced by delayed communication in arrays of diffusively coupled autonomous chemical oscillators.

We study the impact of delayed feedbacks in the collective synchronization of ensembles of identical and autonomous micro-oscillators. To this aim, we consider linear arrays of Belousov-Zhabotinsky (BZ) oscillators confined in micro-compartmentalised systems, where the delayed feedback mimics natural lags that can arise due to the confinement properties and mechanisms driving the inter-oscillator communication. The micro-oscillator array is modeled as a set of Oregonator-like kinetics coupled via mass exchange of the chemical messengers. Changes in the synchronization patterns are explored by varying the delayed feedback introduced in the messenger species Br2. A direct transition from anti-phase to in-phase synchronization and back to the initial anti-phase scheme is observed by progressively increasing the time delay from zero to the value T0, which is the oscillation period characterising the system without any delayed coupling. The route from anti- to in-phase oscillations (and back) consists of regimes where windows of in-phase oscillations are periodically broken by anti-phase beats. Similarities between these phase transition dynamics and synchronization scenarios characterising the coordination of oscillatory limb movements are finally discussed.