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We report the results of time series analysis of blazar PKS 1440-389, observed by the Transiting Exoplanet Survey Satellite (TESS) in two sectors. We find that the source has a quasi-periodic oscillation (QPO) of about 3.1 days for sector 11 and around 3.7 days for sector 38 in the optical band. We use two methods to assess the QPO and its confidence level: Lomb–Scargle periodogram and weighted wavelet Z-transforms. We explore various potential explanations for these rapid quasi-periodic variations and propose that their source most likely resides within the innermost region of the accretion disk. Within this framework, we estimate the mass of the central black hole of this blazar. We obtain black hole masses of 6.65 × 108 M ⊙ (Schwarzschild black hole) and 4.22 × 109 M ⊙ (maximally rotating Kerr black hole), with a main period of 3.7 days. Finally, we utilize the kink instability model to explain the QPO. [ABSTRACT FROM AUTHOR]

Purpose: The bifurcating solution generated by Neimark-Sacker bifurcation of map exhibits a typical quasi-periodic oscillation behavior, which is beneficial for the active use of bifurcation in bifurcation control field. In this paper, an impulsive state feedback control method is proposed to create the quasi-periodic oscillation with certain desired characteristic in the vibro-impact system. Method: The linear control gains determined by using the explicit criteria of Neimark-Sacker bifurcation without directly using eigenvalues are designed to guarantee the existence of quasi-periodic oscillation. On the other hand, the non-linear control gains, which are determined by using center manifold reduction theory and normal form approach, ensure that the created quasi-periodic oscillation is stable. The amplitude of the trajectory section on the torus of quasi-periodic oscillation is analytically derived to achieve the control of the amplitude of invariant torus section by selecting appropriate non-linear control gains. Results and conclusions: Numerical experiments are provided to show the effectiveness of the proposed control method in a two-degree-of-freedom vibro-impact system. The results of quantitative analysis show that a stable quasi-periodic oscillation in the vibro-impact system can be created at a preassigned bifurcation point by desiging linear and nonlinear control gains, and the effect of the nonlinear control gains on the amplitude is either a positive relationship or a negative correlation to the amplitude. [ABSTRACT FROM AUTHOR]

The pursuit of understanding and testing general relativity involves both theoretical and observational efforts. To study the strong gravitational fields near astrophysical black holes and compact objects, which are not directly accessible, researchers often assume that these black holes are described by the Kerr solution. However, there are other objects that can mimic the properties of a black hole, making it challenging to connect theoretical models to observations. Therefore, it is important to explore deviations by introducing small additional parameters as extra physical degrees of freedom in order to establish a link between the models and observational data. This paper presents the development of an alternative background that incorporates these additional parameters. The subsequent analysis includes examining the expected astrophysical properties and validating them through comparison with observational data. [ABSTRACT FROM AUTHOR]

Pattern recognition algorithms are commonly utilized to discover certain patterns, particularly in image-based data. Our study focuses on quasiperiodic oscillations (QPO) in celestial objects referred to as cataclysmic variables (CV). We are dealing with interestingly indistinct QPO signals, which we analyze using a power density spectrum (PDS). The confidence in detecting the latter using certain statistical approaches may come out with less significance than the truth. We work with real and simulated QPO data of a CV called MV Lyrae. Our primary statistical tool for determining confidence levels is sigma intervals. The aforementioned CV has scientifically proven QPO existence, but as indicated by our analysis, the QPO ended up falling below 1 - σ, and such QPOs are not noteworthy based on the former approach. We intend to propose and ultimately train a convolutional neural network (CNN) using two types of QPO data with varying amounts of training dataset lengths. We aim to demonstrate the accuracy and viability of the classification using aCNNin comparison to sigma intervals. The resulting detection rate of our algorithm is very plausible, thus proving the effectiveness of CNNs in this scientific area. [ABSTRACT FROM AUTHOR]

We report the results of time series analysis of blazar PKS 1440-389, observed by the Transiting Exoplanet Survey Satellite (TESS) in two sectors. We find that the source has a quasi-periodic oscillation (QPO) of about 3.1 days for sector 11 and around 3.7 days for sector 38 in the optical band. We use two methods to assess the QPO and its confidence level: Lomb–Scargle periodogram and weighted wavelet Z-transforms. We explore various potential explanations for these rapid quasi-periodic variations and propose that their source most likely resides within the innermost region of the accretion disk. Within this framework, we estimate the mass of the central black hole of this blazar. We obtain black hole masses of 6.65 × 108M⊙ (Schwarzschild black hole) and 4.22 × 109M⊙ (maximally rotating Kerr black hole), with a main period of 3.7 days. Finally, we utilize the kink instability model to explain the QPO.

We consider the hierarchical organization of the parameter space of four coupled phase oscillators. The structure of the complete synchronization and quasi-periodicity regions of different dimensions are studied. The bifurcation mechanisms of destruction of full and partial synchronizations are discussed. [ABSTRACT FROM AUTHOR]

Quasi-periodic oscillation characteristics of a nonlinear energy sink (NES) system under harmonic excitation are studied in this work. It is found that there exist uniformly distributed sidebands in frequency spectra of quasi-periodic oscillations. The traditional incremental harmonic balance (IHB) method and the IHB method with two time-scales are used to obtain accurate frequency components and amplitudes of periodic responses and two different quasi-periodic oscillations of the system, respectively, with variations of the external excitation frequency and amplitude. The two different quasi-periodic oscillation characteristics are analyzed; energy absorption of the NES system under different excitation frequencies and amplitudes is also analyzed. Stability of quasi-periodic solutions obtained from the IHB method with two time-scales is analyzed by the Floquet theory. Analytical results obtained from the traditional IHB method and the IHB method with two time-scales agree very well with those from numerical integration using the fourth-order Runge–Kutta method. Results show that the efficiency of energy absorption of a strongly quasi-periodic oscillation is greater than those of a periodic response and a weakly quasi-periodic oscillation. [ABSTRACT FROM AUTHOR]

Electro-active polymers are often subjected to periodic loading when used as actuators or resonators, thus the dynamical response and the failure of the material subjected to electro-mechanical coupling loading with the effect of temperature are important. The nonlinear thermo-electro-mechanical dynamical response and the failure of an incompressible electro-active polymer cylindrical shell subjected to a suddenly applied constant load or a periodic internal load are analyzed within the framework of finite elasto-dynamics in this paper. The time history curves, phase portraits, Poincare maps of the shell in terms of different pressures, voltages, temperatures or wall thicknesses are presented through numerical computation. The attention is focused on the parameter effect on the motion of the shell and the corresponding critical values. Results indicate that the shell will undergo nonlinear periodic oscillation or quasi-periodic oscillation, and maybe a failure with time if one of the parameters for load, voltage, temperature or wall thickness exceeds its critical value. It is hoped that the results of this paper may provide a numerical reference for the related application and design of diverse electro-active polymers.

The baroclinic annular mode (BAM) is a leading‐order mode of the eddy kinetic energy in the Southern Hemisphere exhibiting oscillatory behaviour at intraseasonal time‐scales. The oscillation mechanism has been linked to transient eddy–mean flow interactions which remain poorly understood. Here we demonstrate that the finite memory effect in eddy‐heat flux dependence on the large‐scale flow can explain the origin of the BAM's oscillatory behaviour. We represent the eddy memory effect by a delayed integral kernel that leads to a generalized Langevin equation for the planetary‐scale heat equation. Using a mathematical framework for the interactions between planetary‐ and synoptic‐scale motions, we derive a reduced dynamical model of the BAM – a stochastically forced oscillator with a period proportional to the geometric mean between the eddy memory time‐scale and the diffusive eddy equilibration time‐scale. Our model provides a formal justification for the previously proposed phenomenological model of the BAM and could be used to explicitly diagnose the memory kernel and improve our understanding of transient eddy–mean flow interactions in the atmosphere. [ABSTRACT FROM AUTHOR]

This paper investigates quasi-periodic oscillations of roll system in corrugated rolling mill in resonance. The two-degree of freedom vertical nonlinear mathematical model of roller system is established by considering the nonlinear damping and nonlinear stiffness within corrugated interface of corrugated rolling mill. In order to investigate the quasi-periodic oscillations at the resonance points, the Poincaré map is established by solving the power series solution of dynamic equations. Based on the Poincaré map, the existence and stability of quasi-periodic oscillations from the Neimark-Sacker bifurcation in the case of resonance are analyzed. The numerical simulation further verifies the correctness of the theoretical analysis.

In the narrow-line Seyfert galaxy (NLS1) ESO 113-G010, two quasi-periodic oscillation (QPO) signals are detected in the XMM-Newton data collected in 2005 November. The XMM-Newton telescope has an exposure longer than 100 ks in the energy range of 0.3–10 keV. The data are analyzed using the Lomb-Scargle periodogram (LSP) and the weighted wavelet Z-transform (WWZ) methods. It is found that there are ∼ 2.24 hour and ∼ 4.09 hour QPOs in the observation with the confidence levels of 7.3 σ and 4.8 σ , respectively. The two QPO signals have a relationship of approximately 1:2 (1:1.83). The absence of QPO in another observation of the object suggests that it is a transient phenomenon. The relationship between the mass of the ESO 113-G010 central black hole (BH) M BH and its frequency f QPO satisfies the known logarithmic linear relation in highly accreting BH systems, from stellar-mass BHs to supermassive BHs. The energy spectrum analysis reveals that the source has a soft X-ray excess below 1 keV. [ABSTRACT FROM AUTHOR]

We study epicyclic oscillatory motion along circular geodesics of the Simpson–Visser meta-geometry describing in a unique way regular black-bounce black holes and reflection-symmetric wormholes by using a length parameter l. We give the frequencies of the orbital and epicyclic motion in a Keplerian disc with inner edge at the innermost circular geodesic located above the black hole outer horizon or on the our side of the wormhole. We use these frequencies in the epicyclic resonance version of the so-called geodesic models of high-frequency quasi-periodic oscillations (HF QPOs) observed in microquasars and around supermassive black holes in active galactic nuclei to test the ability of this meta-geometry to improve the fitting of HF QPOs observational data from the surrounding of supermassive black holes. We demonstrate that this is really possible for wormholes with sufficiently high length parameter l.

In this paper, analysis results of the photometric data of DO Dra will be presented. DO Dra had been observed with 1 m LOAO telescope and 0.6 m CBNUO telescope from 2005 through 2014. The data shows kind of periodic oscillation behavior in the orbital period and also in the spin period. It has been found that these QPOs are not observed always and that the periods vary from 30 min to 80 min. We also found that the period variation seems to repeat itself with the period of 13.5 days. It is essential to monitor this object in the future as well as to carry out model calculation in order to have better understanding of these QPO phenomena.

Abundances of bacterial species such as Escherichia coli in a given environment are partly regulated by predation by protozoa species. Interactions among prey and predator species are not simple since a prey species has acquired defense mechanism against predation. A variety of defense mechanisms are known, for instance, production of toxin as a negative feedback effect to suppress predator species. On the other hand, negative feedback effects can be generated by a predator species to the prey species. The resulting population dynamics under the presence of negative feedback effects would be significantly affected by the strength of feedback control and time delay which naturally occurs until negative feedback effects become effective. In this paper, we develop a mathematical model to investigate the interaction between Shiga-toxin producing Escherichia coli and Tetrahymena with delayed feedback controls by production of Shiga-toxin and recruitment of neutrophils. By applying the quasi-steady-state approximation, the proposed model is reduced to a Lotka-Volterra type predator-prey system with two discrete delays. By investigating the distribution of the roots of the characteristic equation, the local stability as well as Hopf-bifurcation are studied. We provide a clear classification framework to detect the possibility of Hopf-bifurcation when two delays are present. Numerical simulations are carried out to verify the analytical results. Our findings reveal that the instability regions of coexistence equilibrium in two delay parameters plane always enlarge with the increase in negative feedback control coefficients, and especially the feedback controls on Tetrahymena population play a dominant role in the destabilization of coexistence equilibrium. Besides, we observe some interesting phenomena such as peak-adding bifurcation, quasi-periodic oscillation and chaos. [ABSTRACT FROM AUTHOR]

The nonlinear harmonic response of an autoparametric system comprised of a linear oscillator with a vertically attached flexural beam is investigated and the capability of the beam as a vibration absorber is assessed. A weak torsional spring is used for constraining the rotation of the beam giving rise to an almost non-flexural rotational mode with a low frequency. The system parameters are also tuned to enforce the zero-to-one-to-one internal resonance condition. The Lagrange’s formulation accompanied by the assumed-mode method is used to derive the discretized equations based on the order three nonlinear Euler–Bernoulli beam theory. An analytical solution is developed based on the method of multiple scales where the generalized coordinate corresponding to the non-flexural rotational mode is approximated by higher order perturbation expansion than the other coordinates, due to much larger contribution of the non-flexural rotation to the response. Comprehensive response and bifurcation analysis are performed using analytical and direct numerical solutions. The results are obtained for vertically-aligned and also initially inclined beams and various interesting behaviors are recognized for different non-dimensional system parameters. Different types of bifurcations such as the Pitch-fork, Hopf, Period-doubling and symmetry breaking bifurcations are observed in the solution of slow-flow equations and some of them are found to be beneficial for vibration absorption in a limited range of excitation amplitudes and frequencies. [ABSTRACT FROM AUTHOR]

We investigate the effect of horizontal quasi-periodic oscillations on the stability of two immiscible fluids of different densities. The two fluid layers are confined in a cavity of infinite extension in the horizontal directions. We show in the inviscid theory that the linear stability analysis leads to the quasi-periodic Mathieu equation, with damping, which describes the evolution of the interfacial amplitude. Thus, we examine the effect of horizontal quasi-periodic vibration, with two incommensurate frequencies, on the stability of the interface. The numerical study shows the existence of two types of instability: the Kelvin-Helmholtz instability and the quasi-periodic resonances. The numerical results show also that an increase of the frequency ratio has a distabilizing effect on the Kelvin-Helmholtz instability and curves converge towards those of the periodic case.

We study the linear stability of two superposed layers of viscous, immiscible fluids of different densities. The whole system is subject to horizontal quasi-periodic oscillation with two incommensurates frequencies ω1 and ω2. The spectral method and Floquet’s theory combined with Runge-Kutta method are used to solve numericelly the linear problem. We analyse the influence of the frequencies ratioω=ω2ω1$ \omega = {{{\omega _1}} \over {{\omega _2}}} $, on the mariginal stability. The numerical solution shows that the quasi-periodic excitation has a stabilizing or a destabilizing effect on the Kelvin-Helmholtz instability as well as in the parametric resonances depending on the frequency ratio and the amplitudes ratio α=α2α1$ \alpha = {{{\alpha _2}} \over {{\alpha _1}}} $.

In this paper, a numerical study of the dynamic of the non-self-gravitating, unmagnetized, non-axisymmetric, and rotating the torus around the non-rotating black hole is presented. We investigate the instability of the rotating torus subject to perturbations presented by increasing or decreasing the angular velocity of the stable torus. We have done, for the first time, an extensive analysis of the torus dynamic response to the perturbation of the angular velocity of the stable torus. We show how the high, moderate, and low values of the perturbations affect the torus dynamic and help us to understand the properties of the instability and quasi-periodic oscillation (QPO). Our numerical simulations indicate the presence of Papaloizou-Pringle instability (PPI) with global m = 1 mode and QPOs for the moderate and lower values of the perturbations on the angular velocity of the stable torus. Furthermore, with the lower values of the perturbations, the torus can lead to a wiggling initially and then PPI is produced in it. Finally, the matter of the torus would be dissipated due to the presence of a strong torque. [ABSTRACT FROM AUTHOR]

We have performed the numerical simulation of the perturbed relativistic torus around the black hole by solving the general relativistic hydrodynamics equations on the equatorial plane. We have monitored the different simple models by applying the radial and angular velocity perturbations to the steady state torus around the black hole. The instabilities are triggered by adding the subsonic velocity fields over the radial and angular velocities of the stable torus. We have found the disk instability so-called the Papaloizou-Pringle instability and excited modes of the Quasi-Periodic Oscillations (QPOs) in the thin disk approximation case. The significant oscillations and oscillation modes in the mass accretion rates are observed around the rotating black hole with a radial velocity perturbation. The angular velocity perturbation can not create the significant variations and QPOs in the nonselfgravitating relativistic torus around the nonrotating and rotating black holes. The results observed from the radial velocity perturbation might be used to explain the Papaloizou-Pringle instability observed in NGC 1068. [ABSTRACT FROM AUTHOR]

We consider a system of three interacting van der Pol oscillators with reactive coupling. Phase equations are derived, using proper order of expansion over the coupling parameter. The dynamics of the system is studied by means of the bifurcation analysis and with the method of Lyapunov exponent charts. Essential and physically meaningful features of the reactive coupling are discussed. [ABSTRACT FROM AUTHOR]

An analytical model is proposed for the dynamic behavior analysis of a dielectric elastomer (DE) membrane undergoing in-plane stretching. We employ the neo-Hookean model for describing the hyperelasticity feature of the DE membrane. The DE membrane is assumed to elongate only in length direction. For better understanding the dynamic responses of the DE membrane, both free and forced oscillations of the nonlinear system are analyzed. The results show that the system may display periodic oscillations in its length, no matter the DE membrane is constrained by linear or nonlinear cubic springs. It is found that quasi-periodic oscillations of the DE membrane fairly occur provided an in-plane harmonic force is applied. In addition, the response frequencies of the system are also addressed. [ABSTRACT FROM AUTHOR]

The system of a vessel and a direct spring operated pressure relief valve is extended by a downstream pipe. The presented mathematical model consisting of ordinary and partial differential equations can be transformed to a system of differential difference equations by means of the travelling wave solutions of the partial differential equations. This model contains a time delay originated in the pipe length and the speed of sound in the pipe. The linear stability analysis presents stability charts in a parameter plane characterising the environment where the valve is built in. The boundary lines and the corresponding vibration frequencies of the self-excited vibrations are determined as compact closed form expressions. Several analogies are identified with other physical systems modelled by delayed oscillators. Both the stability charts and the vibration frequencies are checked with numerical simulations of the original nonlinear system consisting of coupled ordinary and partial differential equations. The connection between the travelling wave solution and the standard quarter standing wave approximation is explained. A qualitatively relevant phenomenon is identified, namely the appearance of the quasi-periodic vibration at certain parameter combinations. • Construction of delay differential equations for vessel–valve–pipe system. • Closed form stability boundaries and stability charts. • Closed form expressions of vibration frequencies at stability boundaries. • Analytical expression for pipe-length independent stability. • Identification of quasi-periodic oscillations. • Numerical validation of stability charts. [ABSTRACT FROM AUTHOR]

Ensembles of several Rössler chaotic oscillators are considered. It is shown that a typical phenomenon for such systems is the emergence of different and sufficiently high dimensional invariant tori. The possibility of a quasi-periodic Hopf bifurcation and a cascade of such bifurcations based on tori of increasing dimension is demonstrated. The domains of resonance tori are revealed. Boundaries of these domains correspond to the saddle-node bifurcations. Inside the domains of resonance modes, torus-doubling bifurcations and destruction of tori are observed. [ABSTRACT FROM AUTHOR]

In this study, we construct a circuit composed of bistable oscillators and we report the experimental observations of quasi-periodic waves propagating in the circuit and compare them with the associated numerical results. Two different types of propagating quasi-periodic waves with identical parameter sets are experimentally verified. The associated numerical results are distinguished by comparing trajectories on the phase planes and by analyzing the one-parameter bifurcation diagrams. Furthermore, the experiments reveal five different types of switching oscillations. The associated numerical results are also presented, and the stability of the switching oscillations (when constrained to an invariant subspace) is numerically investigated. We also calculate spectral distribution for one type of the switching oscillation. [ABSTRACT FROM AUTHOR]

The dynamics of in-plane tethered subsatellite moving in a circular orbit during station-keeping phase is studied. An attitude motion of the subsatellite is taken into account in this study. The system established by means of Lagrange's equation shows that the motion of in-plane tethered satellite behave as a time-varying nonlinear oscillation, i.e. , there exist the coupled fast and slow motions related to the attitude of the subsatellite and the pitch motion of the tether in the case of small ratio of radius of subsatellite to tether length. In order to gain an understanding of the coupled fast and slow motions, a two variable perturbation method in conjunction with multiple scales of time is proposed to obtain the asymptotic analytical solutions. The analytical and numerical results show that the coupled fast and slow motions of in-plane tethered satellite system in a circular orbit would fall into a quasi-periodic oscillation. [ABSTRACT FROM AUTHOR]

This paper investigates quasi-periodic oscillations of roll system in corrugated rolling mill in resonance. The two-degree of freedom vertical nonlinear mathematical model of roller system is established by considering the nonlinear damping and nonlinear stiffness within corrugated interface of corrugated rolling mill. In order to investigate the quasi-periodic oscillations at the resonance points, the Poincaré map is established by solving the power series solution of dynamic equations. Based on the Poincaré map, the existence and stability of quasi-periodic oscillations from the Neimark-Sacker bifurcation in the case of resonance are analyzed. The numerical simulation further verifies the correctness of the theoretical analysis. [ABSTRACT FROM AUTHOR]

Dynamical responses, such as motion and destruction of hyper-elastic cylindrical shells subject to periodic or suddenly applied constant load on the inner surface, are studied within a framework of finite elasto-dynamics. By numerical computation and dynamic qualitative analysis of the nonlinear differential equation, it is shown that there exists a certain critical value for the internal load describing motion of the inner surface of the shell. Motion of the shell is nonlinear periodic or quasi-periodic oscillation when the average load of the periodic load or the constant load is less than its critical value. However, the shell will be destroyed when the load exceeds the critical value. Solution to the static equilibrium problem is a fixed point for the dynamical response of the corresponding system under a suddenly applied constant load. The property of fixed point is related to the property of the dynamical solution and motion of the shell. The effects of thickness and load parameters on the critical value and oscillation of the shell are discussed. [ABSTRACT FROM AUTHOR]