Complex Oscillations Research Articles

Dynamics of pH Oscillators in Continuous Stirred Tanks in Series.

Complex reaction networks with positive and negative feedback can produce diverse nonlinear phenomena in open reactors, such as multistability and oscillations. pH oscillators driven by hydrogen or hydroxide autocatalytic processes show sustained oscillations in continuously stirred tank reactors (CSTR) but only a sharp pH switch in batch. Here, we present a numerical study on the dynamics of pH oscillators in a series of CSTRs. We show a critical residence time under which bistability and above which oscillations develop. The dynamics of the CSTR cascade show the cross-shaped phase diagram of nonlinear activatory inhibitory systems. In the domain of oscillations, one reactor starts to oscillate autonomously and induces forced complex oscillations in the following tanks with damped amplitudes. These results, with their practical implications, may contribute to understanding the recent experimental observations of nonlinear phenomena in the presence of a residence time ramp and inspire further research in this area.

Inferring the Accurate Locations of Noise Records in Mobile Phone Location Data

ABSTRACTThe positioning uncertainty of mobile phone location (MPL) data greatly influences location services and crowd behavior analysis. Although many achievements have been made in controlling its main sources (signal drift and ping‐pong effects), several problems, such as single‐oscillation patterns, insufficient position optimization, and a lack of effective evaluation, remain. In this study, a set of MPL data quality optimization methods are proposed. First, the characteristics of drift records and the oscillation patterns of ping‐pong records are discussed. The quality of the MPL data is subsequently controlled with the proposed feature‐based drift‐record detection method, complex oscillation pattern‐based ping‐pong‐record detection method, and cumulative duration weighting‐based ping‐pong‐record optimization method. These methods are applied to the MPL dataset of a major operator in Nanjing city, and the optimization effect is evaluated with GPS data collected synchronously. The results show that the proposed detection and optimization methods can effectively improve the accuracy of MPL data.

PERIODIC ATEB-FUNCTIONS AND THE VAN DER POL METHOD FOR CONSTRUCTING SOLUTIONS OF TWO-DIMENSIONAL NONLINEAR OSCILLATIONS MODELS OF ELASTIC BODIES

In the process of operation, the simplest elements (hereinafter elastic bodies) of machines and mechanisms under the influence of external and internal factors carry out complex oscillations ‒ a combination of longitudinal, bending and torsion combinations in various combinations. In general, mathematical models of the process of such complex phenomena in elastic bodies, even for one-dimensional calculation models, are boundary value problems for systems of partial differential equations. A two-dimensional mathematical model of oscillatory processes in a nonlinear elastic body is considered. A method of constructing an analytical solution of the corresponding boundary-value problems for nonlinear partial differential equations is proposed, which is based on the use of Ateba functions, the Van der Pol method, ideas of asymptotic integration, and the principle of single-frequency oscillations. For "undisturbed" analogues of the model equations, single-frequency solutions were obtained in an explicit form, and for "perturbed" ‒ analytical dependences of the basic parameters of the oscillation process on a small perturbation. The dependence of the main frequency of oscillations on the amplitude and non-linearity parameter of elastic properties in the case of single-frequency oscillations of "unperturbed motion" is established. An asymptotic approximation of the solution of the autonomous "perturbed" problem is constructed. Graphs of changes in amplitude and frequency of oscillations depending on the values of the system parameters are given.

Three-Dimensional Analysis of Vocal Fold Oscillations: Correlating Superior and Medial Surface Dynamics Using Ex Vivo Human Hemilarynges.

The primary acoustic signal of the voice is generated by the complex oscillation of the vocal folds (VFs), whereby physicians can barely examine the medial VF surface due to its anatomical inaccessibility. In this study, we investigated possibilities to infer medial surface dynamics by analyzing correlations in the oscillatory behavior of the superior and medial VF surfaces of four human hemilarynges, each in 24 different combinations of flow rate, VF adduction, and elongation. The two surfaces were recorded synchronously during sustained phonation using two high-speed camera setups and were subsequently 3D-reconstructed. The 3D surface parameters of mean and maximum velocities and displacements and general phonation parameters were calculated. The VF oscillations were also analyzed using empirical eigenfunctions (EEFs) and mucosal wave propagation, calculated from medial surface trajectories. Strong linear correlations were found between the 3D parameters of the superior and medial VF surfaces, ranging from 0.8 to 0.95. The linear regressions showed similar values for the maximum velocities at all hemilarynges (0.69-0.9), indicating the most promising parameter for predicting the medial surface. Since excessive VF velocities are suspected to cause phono-trauma and VF polyps, this parameter could provide added value to laryngeal diagnostics in the future.

Derivation of analytic formulae for several resonance frequencies of the SparkJet actuator

Building on previous research that emphasized the importance of focusing on resonance frequencies for a fundamental understanding of the thrust and complex internal flow phenomena of the SparkJet actuators, this study theoretically derives analytic formulae for several important resonance frequencies. The research addresses the typical configuration of the SparkJet actuators, which consists of a cylindrical cavity and orifice connected by a conical converging nozzle. While the resonance frequencies of the SparkJet actuators can be obtained by solving the eigenvalue problem presented in previous studies, this eigenvalue problem, despite being a typical boundary value problem in the form of an elliptic partial differential equation, is challenging to solve using conventional numerical methods such as iterative methods, because the eigenvalue is included as an unknown in the operator. Consequently, Boundary Element Method (BEM) or methods using the Green functions have been proposed to obtain numerical solutions, but these still require handling large matrix data, resulting in significant computational costs and memory consumption. To overcome this, the current study first simplifies the eigenvalue problem using the conformal mapping presented in previous research. Then, referencing prior studies that claim that three types of resonance frequencies (Helmholtz resonance frequency and resonance frequencies representing streamwise or radial directional oscillation) significantly affect the thrust of the SparkJet actuators, characteristics of these frequencies are mathematically defined. Using these mathematical characteristics, the study derives the asymptotic and approximate solutions of the simplified eigenvalue problem, from which the resonance frequencies are obtained. The analytic formulae proposed in this study theoretically explain the already known geometric tendencies of the resonance frequencies and reveal new geometric factors influencing resonance frequencies, which were previously unknown. This approach is expected to facilitate obtaining several important resonance frequencies of the SparkJet actuator more promptly and accurately and to provide a deeper understanding of the nature of the complex oscillation phenomena inside the actuator.

Numerical study on flow instability in parallel helical tubes under ocean conditions

The superimposed coupling of flow oscillations generated by transient external forces under ocean conditions and flow oscillations in parallel helical tubes during two-phase flow instability may lead to more complex flow oscillation phenomena in parallel helical tubes. However, there is still a lack of understanding regarding the effect of ocean conditions on the two-phase flow instability within parallel helical tubes. The two-phase flow instability in parallel helical tubes under ocean conditions is numerically investigated in the present study. The effects of ocean conditions on the flow behavior and instability threshold in parallel helical tubes are studied with mass flux 200 kg/m2s and inlet subcooling within 5–70 °C. The results show that the mass flow rate decreases as the inclination angle increases. A larger rolling amplitude or shorter period increases the flow and temperature oscillation amplitude. Two characteristic frequencies are found in the natural circulation flow instability under the rolling motion. As the rolling amplitude increases, the compound flow oscillation amplitude is larger and more chaotic with a certain phase shift. The effect of stationary inclining on the flow instability threshold is rather significant than rolling effect. The results of the present study can serve as a significant reference for the operation and design of the helical-coiled once-through steam generator under ocean conditions.

SPATIOTEMPORAL DYNAMICS IN A MODEL OF IMMUNODOMINANCE

Adapative immune response to viral infection is mediated by cytotoxic T-lymphocytes (CTLs) eliminating infected cells and virus-neutralizing antibodies produced by B-lymphocytes. Different epitopes, that is, some parts of antigens, stimulate clonal expansion of the corresponding lymphocytes. These different types of CTLs and antibodies begin to compete with each other leading to immunodominance of some of them. As a result, some types of CTLs and antibodies will persist and increase their number, while some others will become extinct. In this work, we study spatiotemporal dynamics in a previously developed mathematical model of immunodominance. We begin with the investigation of complex oscillations exhibited by the concentrations of epitopes and corresponding cytotoxic T-lymphocytes in the ODE model and determine the mechanism of these oscillations. After that, we study the reaction–diffusion system of equations describing their spatiotemporal dynamics and analyze how these dynamics depend on the interaction of different virus variants and CTL types.

Multilevel dynamics of matter waves scattering in finite potential wells

We explore the dynamics of matter wave scattering in finite potential wells using analytical solutions of the Schrödinger equation within the framework of a quantum shutter model. We find that the incident wave interferes with the bound states of the quantum well, resulting in time-domain oscillations. These oscillations exhibit Rabi-type frequencies, characterised by the energy differences between the incident wave and the bound states of the quantum well. We show that in systems with double-bound states, the interference pattern is characterised by quantum beats in the time-dependent probability density. The period of these beatings depends on the energy difference between the bound states, which can be tuned by controlling the potential parameters. In the general case where bound, anti-bound, and resonant states coexist in the system spectrum, complex oscillations in the probability density arise from the interactions of the incident wave with different quantum states. We demonstrate that the bound states sector can effectively describe this complex behaviour, providing a simple and reliable analytical expression for the probability density in multilevel systems. This formula highlights the significant role of bound states, whose interaction with the incident wave dominates the transient probability density. This contrasts with conventional systems with potential barriers and wells, where resonances govern the wave dynamics.

DEVELOPMENT OF MODELS COMPLEX OSCILLATIONS FOR AUTOMATION SYSTEMS OF VIBROACOUSTIC OPERATIONAL SAFETY CONTROL OF BUILDINGS AND STRUCTURES

Problem statement. Long-term safe operation of buildings and structures is impossible without determining the stability of their load-bearing elements, especially after shocks and dynamic loads under the influence of explosions and fires. In such conditions, reliable and productive monitoring of the reliability of buildings and structures is a critical element in increasing human safety. Vibroacoustic is an effective and informative method that allows for non-destructive assessment of the condition of concrete, reinforced concrete, brick, multi-layer walls and other types of structures. However, to increase the speed and quality of determining the state of objects, maximum automation of the vibroacoustic method is required. Purpose of the study. Increasing the productivity and reliability of vibroacoustic monitoring of buildings and structures by automating the impact action with specified parameters based on the development of dynamic models of complex oscillations. Methods. Analytical studies of dynamic and kinematic models of the exciter of mechanical vibrations, computer modeling, laboratory tests of the vibration generator control system. Research results. Models of complex oscillations have been developed to improve reliability and implement new control laws that are impossible for classical vibration systems and are necessary for automated vibroacoustic control of buildings and structures and ensure the safety of their operation. The use of reduced bit depth coefficients in the calculation scheme using the Jack W. Crenshaw algorithm is justified in a wider range of argument values than with initial coefficient values for controlling vibration systems with limited computational performance. This is necessary when creating executive bodies of modern systems for automated vibroacoustic monitoring of the cracks and violations of the homogeneity of load-bearing structures of buildings and structures. The oscillation exciter has been tested in laboratory conditions. Scientific novelty. New methods and algorithms for automatic control of vibration exciters have been developed to obtain polyfrequency oscillations, linear waves and wave fields with specified amplitude and frequency characteristics. Practical significance. An oscillation exciter has been developed for a system of automated vibroacoustic control of the buildings and structures operation safety. This provides a necessary and sufficient basis for improving methods for assessing changes in the environment as a result of the appearance of cracks and loss of homogeneity.

Mechanical and biochemical feedback combine to generate complex contractile oscillations in cytokinesis

The actomyosin cortex is an active material that generates force to drive shape changes via cytoskeletal remodeling. Cytokinesis is the essential cell division event during which a cortical actomyosin ring closes to separate two daughter cells. Our active gel theory predicted that actomyosin systems controlled by a biochemical oscillator and experiencing mechanical strain would exhibit complex spatiotemporal behavior. To test whether active materials invivo exhibit spatiotemporally complex kinetics, we imaged the C.elegans embryo with unprecedented temporal resolution and discovered that sections of the cytokinetic cortex undergo periodic phases of acceleration and deceleration. Contractile oscillations exhibited a range of periodicities, including those much longer periods than the timescale of RhoA pulses, which was shorter in cytokinesis than in any other biological context. Modifying mechanical feedback invivo or in silico revealed that the period of contractile oscillation is prolonged as a function of the intensity of mechanical feedback. Fast local ring ingression occurs where speed oscillations have long periods, likely due to increased local stresses and, therefore, mechanical feedback. Fast ingression also occurs where material turnover is high, invivo and in silico. We propose that downstream of initiation by pulsed RhoA activity, mechanical feedback, including but not limited to material advection, extends the timescale of contractility beyond that of biochemical input and, therefore, makes it robust to fluctuations in activation. Circumferential propagation of contractility likely allows for sustained contractility despite cytoskeletal remodeling necessary to recover from compaction. Thus, like biochemical feedback, mechanical feedback affords active materials responsiveness and robustness.

Dynamical analysis of a periodically forced chaotic chemical oscillator.

We present a comprehensive dynamical analysis of a chaotic chemical model referred to as the autocatalator, when subject to a periodic administration of one substrate. Our investigation encompasses the dynamical characterization of both unforced and forced systems utilizing isospikes and largest Lyapunov exponents-based parameter planes, bifurcation diagrams, and analysis of complex oscillations. Additionally, we present a phase diagram showing the effect of the period and amplitude of the forcing signal on the system's behavior. Furthermore, we show how the landscapes of parameter planes are altered in response to forcing application. This analysis contributes to a deeper understanding of the intricate dynamics induced by the periodic forcing of a chaotic system.

Exploring the interplay of intrinsic fluctuation and complexity in intracellular calcium dynamics

The concentration of intracellular calcium ion (Ca2＋) exhibits complex oscillations, including bursting and chaos, as observed experimentally. These dynamics are influenced by inherent fluctuations within cells, which serve as crucial determinants in cellular decision-making processes and fate determination. In this study, we systematically explore the interplay between intrinsic fluctuation and the complexity of various dynamic states of intracellular cytosolic Ca2＋. To investigate this interplay, we employ complexity measures such as permutation entropy and statistical complexity. Using a stochastic chemical Langevin equation, we simulate the dynamics of cytosolic Ca2＋. Our findings reveal that permutation entropy and statistical complexity effectively characterize the diverse, dynamic states of cytosolic Ca2＋ and illustrate their interactions with intrinsic fluctuation. Permutation entropy analysis elucidates that the chaotic state is more sensitive to intrinsic fluctuation than the other periodic states. Furthermore, we identify distinct states of cytosolic Ca2＋ occupying specific locations within the theoretical bounds of the complexity–entropy causality plane. These locations indicate varying complexity and information content as intrinsic fluctuation varies. When adjusting the permutation order, the statistical complexity measure for the different periodic and chaotic states exhibits peaks in an intermediate range of intrinsic fluctuation values. Additionally, we identify scale-free or fractal patterns in this intermediate range, which are further corroborated by multifractal detrended fluctuation analysis. These high-complexity states likely correspond to optimal Ca2＋ dynamics with biological significance, revealing rich and complex dynamics shaped by the interplay of intrinsic fluctuation and complexity. Our investigation enhances our understanding of the intricate regulatory mechanisms governing intracellular Ca2＋ dynamics and how intrinsic fluctuation modulates the complexity of the various dynamics that play crucial roles in biological cells.

Mixed-mode oscillations of an atomic force microscope in tapping mode.

In the phenomenon of mixed-mode oscillations, transitions between large-amplitude and small-amplitude oscillations may lead to anomalous jitter in the probe of a tapping mode atomic force microscope (TM-AFM) during the scanning process, thereby affecting the accuracy and clarity of the topographical images of the tested sample's surface. This work delves deeply into various mixed-mode oscillations and the corresponding formation mechanisms in TM-AFM under low-frequency resonant excitation. Through a detailed analysis of bifurcation sets of the fast subsystem, we found that the system's mixed-mode oscillations encompass the typical two coexisting branches and the novel three coexisting branches of equilibrium point attractors. In the stable case, a certain transition pattern in phase trajectory can be observed involving two jumps and four jumps, switching between quiescent and spiking states. In the bi-stable case, the trajectory undergoes distinct transitions decided by whether to pass through or crossover the middle branch of attractors when bifurcation occurs. By applying basin of attraction and fast-slow analysis methods, we unfold the dynamic mechanism of mixed-mode oscillations with distinct switching patterns. Our research contributes to a better understanding of complex oscillations of TM-AFM and provides valuable insights for improving image quality and measurement precision while mitigating detrimental oscillations.

Chaos in inhomogeneous neutrino fast flavor instability

In dense neutrino gases, the neutrino-neutrino coherent forward scattering gives rise to a complex flavor oscillation phenomenon not fully incorporated in simulations of neutron star mergers (NSM) and core collapse supernovae (CCSNe). Moreover, it has been proposed to be chaotic, potentially limiting our ability to predict neutrino flavor transformations in simulations. To address this issue, we explore how small flavor perturbations evolve in the nonlinear regime of the neutrino quantum kinetic equation within a narrow centimeter-scale region inside a NSM and a toy neutrino distribution. Our findings reveal that paths in the flavor state space of solutions with similar initial conditions diverge exponentially, exhibiting chaos. This inherent chaos makes the microscopic scales of neutrino flavor transformations unpredictable. However, the domain-averaged neutrino density matrix remains relatively stable, with chaos minimally affecting it. This particular property suggests that domain-averaged quantities remain reliable despite the exponential amplification of errors. Published by the American Physical Society 2024

Study on the Bouncing Process Induced by Ice Shedding on Overhead Conductors under Strong Wind Conditions

Strong winds can lead to more complex ice shedding oscillation processes for overhead conductors, inducing flashovers, strand breakages and other accidents. This study analyzes the aerodynamic parameters of several typical icing features and establishes a numerical model for ice shedding on overhead conductors under strong wind conditions. The results show that for the same amount of icing, the resistance and lift force on the conductor changes with ice shape, wind attack angle and wind speed, which has a significant effect on the ice shedding jumping process. When the wind attack angle approaches 180°, the airflow resistance of the fan-shaped and D-shaped icing conductors significantly increases. And in the process of ice shedding response of transmission lines, the lateral amplitude may exceed 20 m, which increase the discharge risk of horizontally arranged conductors. Moreover, for the significant lateral oscillation of conductors by ice shedding under strong wind, the maximum horizontal displacement is approximately 1.6 times the difference in lateral position before and after ice shedding.

Generation of 'semi-guided' cortical organoids with complex neural oscillations.

Temporal development of neural electrophysiology follows genetic programming, similar to cellular maturation and organization during development. The emergent properties of this electrophysiological development, namely neural oscillations, can be used to characterize brain development. Recently, we utilized the innate programming encoded in the human genome to generate functionally mature cortical organoids. In brief, stem cells are suspended in culture via continuous shaking and naturally aggregate into embryoid bodies before being exposed to media formulations for neural induction, differentiation and maturation. The specific culture format, media composition and duration of exposure to these media distinguish organoid protocols and determine whether a protocol is guided or unguided toward specific neural fate. The 'semi-guided' protocol presented here has shorter induction and differentiation steps with less-specific patterning molecules than most guided protocols but maintains the use of neurotrophic factors such as brain-derived growth factor and neurotrophin-3, unlike unguided approaches. This approach yields the cell type diversity of unguided approaches while maintaining reproducibility for disease modeling. Importantly, we characterized the electrophysiology of these organoids and found that they recapitulate the maturation of neural oscillations observed in the developing human brain, a feature not shown with other approaches. This protocol represents the potential first steps toward bridging molecular and cellular biology to human cognition, and it has already been used to discover underlying features of human brain development, evolution and neurological conditions. Experienced cell culture technicians can expect the protocol to take 1 month, with extended maturation, electrophysiology recording, and adeno-associated virus transduction procedure options.

A holistic understanding of optical properties in amorphous H-terminated Si-nanostructures: Combining TD-DFT with AIMD

Silicon, traditionally known as an indirect band gap semiconductor, unveils intriguing properties at the nanoscale, stemming from deviations from k-conservation rules within nanostructures. In our study, we scrutinized four hydrogenated Si 0D-nanostructures—Si10H16, Si14H20, Si18H24, and Si22H28—to unravel their dynamic stability under thermal fluctuations and optical characteristics. We initiated our exploration by employing the TD-DFT framework to generate and analyze the optical properties of these geometrically optimized nanostructures. Simultaneously, we conducted ab initio molecular dynamics simulations to examine the structural robustness and thermal stability of the four structures. Leveraging the Car-Parrinello molecular dynamics approach within the Quantum ESPRESSO open software suite, we observed temperature evolution and stability differences among the nanostructures at targeted temperatures 40 and 300 K. Our subsequent investigation delved into the Turbo-Lanczos time-dependent DFT method, unraveling the optical properties and excited-state dynamics of hydrogenated Si nanostructures. The results unveiled shifts towards higher energy absorption edges E0, accompanied by alterations in the permittivity tensor, complex refractive index, oscillator strength, and reflectivity. Notably, the analysis revealed an enlarged HOMO-LUMO gap, distinctive from bulk Si. Furthermore, our models predicted the elimination of phase-dependent E1/E2 optical transition peaks in the imaginary part of the dielectric function, and a gradual decrease in the low-frequency dielectric response with increased hydrogenation of the amorphous structures. These findings underscore the promising applications of hydrogenating Si nanostructures in diverse technological domains such as optoelectronics, memristors, sensors, and quantum computing. Their tunable optical properties, size-dependent behaviors, and compatibility with existing silicon-based devices make them particularly appealing for next-generation technologies.

Game theory based finite-time formation control using artificial potentials for tethered space net robot

The Tethered Space Net Robot (TSNR) is an innovative solution for active space debris capture and removal. Its large envelope and simple capture method make it an attractive option for this task. However, capturing maneuverable debris with the flexible and elastic underactuated net poses significant challenges. To address this, a novel formation control method for the TSNR is proposed through the integration of differential game theory and robust adaptive control in this paper. Specifically, the trajectory of the TSNR is obtained through the solution of a real-time feedback pursuit-evasion game with a dynamic target, where the primary condition is to ensure the stability of the TSNR. Furthermore, to minimize tracking errors and maintain a specific configuration, a robust adaptive formation control scheme with Artificial Potential Field (APF) based on a Finite-Time Convergent Extended State Observer (FTCESO) is investigated. The proposed control method has a key advantage in suppressing complex oscillations by a new adaptive law, thus precisely maintaining the configuration. Finally, numerical simulations are performed to demonstrate the effectiveness of the proposed scheme.

Dynamical Model of Rotation and Orbital Coupling for Deimos

This paper introduces a novel dynamical model, building upon the existing dynamical model for Deimos in the current numerical ephemerides, which only encompasses the simple libration effects of Deimos. The study comprehensively incorporates the rotational dynamics of Deimos influenced by the torque exerted by the major celestial bodies (Mars, the Sun) in the solar system within the inertial space. Consequently, a full dynamical model is formulated to account for the complete coupling between the rotation and orbit of Deimos. Simultaneously, employing precision orbit determination methods used for artificial satellites, we develop an adjustment model for fitting data to the complete model. The 12-order Adams–Bashforth–Moulton (ABM) integration algorithm is employed to synchronously integrate the 12 state variables of the full model to obtain the orbit of Deimos.The difference in the orbits obtained by integrating the full model over a period of 10 years and those obtained by the simplified model is at the order of 10 km. After precise orbit determination, this difference decreases to below 100 m, so numerical simulation results indicate that the full dynamical model and adjustment model are stable and reliable. Simultaneously, the integration of the Deimos third-order gravity field in the full model over a 10-year period induces only meter-level positional changes. This suggests that when constructing the complete model, the utilization of a second-order gravity field alone is sufficient. Compared to the simple model, the polar axis of Deimos in the inertial space exhibits a more complex oscillation in the full model. Additionally, the full model calculates that the minimum moment of inertia principal axis of Phobos has an amplitude of approximately 0.5 degrees in the longitude direction and does not exceed 2 degrees in the latitude direction. This work further advances the current dynamical model for Deimos and establishes the foundational model for the generation of a new set of precise numerical ephemerides for Deimos.

Oscillation Effects of Innovation on Employment

On the cusp of a promising era of technological progress and innovation that seeks to deeply alter the essence of employment, recent research indicates that there is no straightforward answer to how these changes will affect the total labour force. This study endeavours to clarify the complex oscillations between these forces. It employs a robust methodological fusion of theoretical frameworks and empirical scrutiny to dissect the innovation-employment nexus within both OECD and non-OECD economies. A dynamic regression model was utilized, integrating employment variables through the total labour force, and innovation metrics through the Innovation Program 5 for OECD countries, along with the Patent Cooperation Treaty for non-OECD countries. The analysis favoured the robust two-step SYS-GMM estimator over various estimations, including the DIF-GMM, uncovering a positive relationship effect between innovation and employment. Specifically, the study reveals that the IP5 exerts a significant positive effect on the labour force within OECD countries, endorsing the labour-friendly nature of innovation. Conversely, the PCT demonstrates a marked beneficial effect on employment in non-OECD countries. These insights shed light on the nuanced and favourable interplay between innovation and employment across diverse economies, accentuating the temporal and interdependent nature of their association. The need for in-depth knowledge of innovation and its specific effects on employment is crucial for policy-makers. This entails the development of tailored policies and strategic plans intended for the patenting and exploiting innovations aiming at strengthening employment in its economic environment, in specific business environments and taking account of temporal and contextual factors.