Stochastic Oscillations Research Articles

Stochastic Canards in a Modified Leslie–Gower Population Model

The problem of analyzing the bifurcation mechanisms of complex stochastic oscillations in population dynamics is considered. We study this problem on the basis of the modified Leslie–Gower prey–predator model with randomly forced Holling-II functional response. The paper focuses on the effects of noise in the Canard explosion zone. The phenomenon of noise-induced splitting of Canard cycles is discovered and studied in terms of stochastic [Formula: see text]-bifurcations. In parametric analysis, we use the stochastic sensitivity technique with the apparatus of confidence domains to find the most noise-sensitive Canard. For the phenomenon of stochastic splitting, an underlying deterministic mechanism using critical curves near the cycle orbit and sub-/super-critical zones is revealed.

Stock Market Prediction Using Fuzzy Logic and Technical Indicators: A Case Study of Indian Banks

This study presents a decision support system for stock market investors that combines technical analysis with fuzzy logic. The system utilizes four essential technical indicators—Moving Average Convergence/Divergence (MACD), Relative Strength Index (RSI), Stochastic Oscillator (SO), and On-Balance Volume (OBV)—to predict future price movements. These indicators are mapped as inputs into a fuzzy inference system, where fuzzy rules and membership functions are applied to generate trading recommendations, categorized as Bullish, Neutral, or Bearish. Experiments using MATLAB with data from 10 Indian banks demonstrate that the system effectively predicts stock movements and improves investment decisions when integrated with additional market information and investor insights

Real-time anomaly detection of the stochastically excited systems on spherical ([formula omitted]) manifold

Advanced analytical tools have become crucial in today’s constantly changing and complex systems. Real-time Principal Geodesic Analysis (RPGA) is a novel technique that provides a unique perspective for analyzing nonlinear data on differentiable manifolds. Traditional linear methods are often inadequate when exploring the complexities of such data. Orthogonal transformation techniques such as Principal Component Analysis (PCA) and Principal Geodesic Analysis (PGA) are highly desirable for condition monitoring stochastically excited systems in domains like mechanical, aerospace, and civil engineering. However, uncertainties and dynamic fluctuations necessitate robust analytical methods for early change detection to ensure safety, performance, and cost-effectiveness. Limitations posed by linear orthogonal transformation techniques such as PCA and its recursive counterparts make it imperative to adapt these techniques to nonlinear situations where data does not evolve in a flat Euclidean space. Significant advancements have been made in this field over recent decades, with data-driven real-time algorithms such as RPCA, RCCA, and RSSA providing reliable solutions for complex multidimensional problems. However, for curved space, the nonlinear RPGA technique takes center stage. It is known for its effectiveness in extracting meaningful information from the complex data stream. This paper explores the foundational concepts and methodologies underlying the transition from linear to nonlinear data analysis. By examining examples such as stochastic geometric oscillator on S2, and the inverted spherical pendulum cart system navigating a rough surface, we illustrate the significance of reliable, real-time damage detection techniques provided by tools such as RPGA.

Biomolecular Neuristors from Functionalized Lipid Membranes

AbstractModeled after biological neurons, neuristors are emerging hardware that generate recurring voltage spikes in response to electrical stimulation. This type of excitability can enable transistor‐free spiking neural networks for efficient signal processing and computing. Yet, most neuristors consist of circuits containing numerous devices, thus complicating fabrication and increasing size, power usage, and cost. In contrast, it is shown that a single, 5nm‐thick lipid membrane functionalized with voltage‐activated peptides functions as a two‐terminal, ultra‐low power (fW‐pW) artificial neuristor in response to supplied current. Specifically, the biomolecular membrane generates stochastic voltage oscillations (10–150 mV) in response to direct currents (|5–40| pA), and is capable of generating two distinct types of action potentials fast (≈1–50 ms) and slow (≈1–2 s) spikes via distinct physical mechanisms. This discovery showcases the inherent multifunctionality and modularity of engineered biomembranes, and it contributes to an expanding suite of ionic and biomolecular devices designed with synapse and neuron functionalities for emerging computing architectures.

Precision forecasting in perilous times: stock market predictions leveraging google trends and momentum indicators during COVID-19

PurposeThis study explores the complex impact of COVID-19 on India's financial sector, moving beyond simplistic public health vs. economy views. We assess market vulnerabilities and analyze how public sentiment, measured through Google Trends, can predict stock market fluctuations. We propose a novel framework using Google Trends for financial sentiment analysis, aiming to improve understanding and preparedness for future crises.Design/methodology/approachHybrid approach leverages Google Trends as sentiment tool, market data, and momentum indicators like Rate of Change, Average Directional Index and Stochastic Oscillator, to deliver accurate, market insights for informed investment decisions during pandemic.FindingsOur study reveals that the pandemic significantly impacted the Indian financial sector, highlighting its vulnerabilities. Capitalizing on this insight, we built a ground-breaking predictive model with an impressive 98.95% maximum accuracy in forecasting stock market values during such events.Originality/valueTo the best of authors knowledge this model's originality lies in its focus on short-term impact, novel data fusion and methodology, and high accuracy.• Focus on short-term impact: Our model uniquely identifies and quantifies the fleeting effects of COVID-19 on market behavior.• Novel data fusion and framework: A novel framework of sentiment analysis was introduced in the form of Trend Popularity Index. Combining trend popularity index with momentum offers a comprehensive and dynamic approach to predicting market movements during volatile periods.• High predictive accuracy: Achieving the prediction accuracy (98.93%) sets this model apart from existing solutions, making it a valuable tool for informed decision-making.

Quadrature Based Neural Network Learning of Stochastic Hamiltonian Systems

Hamiltonian Neural Networks (HNNs) provide structure-preserving learning of Hamiltonian systems. In this paper, we extend HNNs to structure-preserving inversion of stochastic Hamiltonian systems (SHSs) from observational data. We propose the quadrature-based models according to the integral form of the SHSs’ solutions, where we denoise the loss-by-moment calculations of the solutions. The integral pattern of the models transforms the source of the essential learning error from the discrepancy between the modified Hamiltonian and the true Hamiltonian in the classical HNN models into that between the integrals and their quadrature approximations. This transforms the challenging task of deriving the relation between the modified and the true Hamiltonians from the (stochastic) Hamilton–Jacobi PDEs, into the one that only requires invoking results from the numerical quadrature theory. Meanwhile, denoising via moments calculations gives a simpler data fitting method than, e.g., via probability density fitting, which may imply better generalization ability in certain circumstances. Numerical experiments validate the proposed learning strategy on several concrete Hamiltonian systems. The experimental results show that both the learned Hamiltonian function and the predicted solution of our quadrature-based model are more accurate than that of the corrected symplectic HNN method on a harmonic oscillator, and the three-point Gaussian quadrature-based model produces higher accuracy in long-time prediction than the Kramers–Moyal method and the numerics-informed likelihood method on the stochastic Kubo oscillator as well as other two stochastic systems with non-polynomial Hamiltonian functions. Moreover, the Hamiltonian learning error εH arising from the Gaussian quadrature-based model is lower than that from Simpson’s quadrature-based model. These demonstrate the superiority of our approach in learning accuracy and long-time prediction ability compared to certain existing methods and exhibit its potential to improve learning accuracy via applying precise quadrature formulae.

Two Distinct Transitions in a Population of Coupled Oscillators with Turnover: Desynchronization and Stochastic Oscillation Quenching.

Synchronization, which is caused by mutual coupling, and turnover, which is the replacement of old components with new ones, are observed in various open systems consisting of many components. Although these phenomena can co-occur, the interplay of coupling and turnover has been overlooked. Here, we analyze coupled phase oscillators with turnover and reveal that two distinct transitions occur, depending on both coupling and turnover: desynchronization and what we name stochastic oscillation quenching. Importantly, the latter requires both the turnover and coupling to be sufficiently intense.

Combined Impact of Multidelay Feedback Number and Interval: A Novel Mechanism for Controlling the Stability of Stochastic Duffing Systems

In this paper, we study a class of nonlinear stochastic Duffing oscillators with multidelay feedback. We propose an effective reduction approach with the help of center manifold theory and stochastic averaging method. Taking the initial time-delay [Formula: see text] as the parameter, we reduce the original system to a one-dimensional averaged Itô equation. Our analysis reveals that the original system exhibits stochastic bifurcations, including stochastic D and P bifurcations. Once we have a clear understanding of the bifurcation structure, we can use this knowledge to choose appropriate system parameters and place the system in the desired state. For instance, by adjusting the initial time-delay [Formula: see text] of the control system, we can stabilize the system and achieve the desired outcome. Numerical simulations also verify the theoretical results. With appropriate parameter choices, multiple time delays can destabilize the equilibrium and promote chaotic behaviors, and can also lead to more stable dynamical behavior. Remarkably, we discovered that increasing the interval of time delays and feedback numbers can enhance system stability. It may potentially serve as a novel mechanism for stabilizing stochastic systems. The study provides a solid theoretical foundation for exploring stochastic systems subject to complex time-delay feedback control, and offers a valuable framework for related fields.

Efektifitas Penggunaan Analisis Stochastic Oscillator Dan Moving Average Convergence-Divergence Pada Perdagangan Saham-Saham Perbankan di Bursa Efek Indonesia

The objective of the research is to find out how effective stochastic oscillator and moving average convergence-divergence (MACD) technical analysis is in yielding capital gain and abnormal return, viewed from descriptive analysis, analysis of effects, and disparity test analysis by using some theories and previous research results. This research uses daily stock closing price data from the issuers in banking su-sector of the research period of 2015-2019. The research employs descriptive analytic approach, regression analysis and disparity test, supported by IBM SPSS version 25 software. The result of the descriptive analysis shows that buy and sell stochastic oscillator and MACD signals are effective in yielding capital gain. The result of regression analysis shows that gain signal yielded by indicator of Stochastic Oscillator and MACD has significant effects on capital gain in which the probability value (Asymp. Sig) of Stochastic Oscillator on capital gain is 0.000, and the probability value (Asymp.Sig) of MACD on capital gain is 0.000. The result of the disparity test analysis shows that there is no difference in abnormal return in the pre and post appearance of gain signal in Stochastic Oscillator and in MACD

Reduced-order dynamics of coupled self-induced stochastic resonance quasiperiodic oscillators driven by varying noise intensities

Reduced-order dynamics of coupled self-induced stochastic resonance quasiperiodic oscillators driven by varying noise intensities

Reliability of early warning indicators of critical transition in stochastic Van der Pol oscillators with additive correlated noise

Reliability of early warning indicators of critical transition in stochastic Van der Pol oscillators with additive correlated noise

Exact Power Spectrum in a Minimal Hybrid Model of Stochastic Gene Expression Oscillations

Exact Power Spectrum in a Minimal Hybrid Model of Stochastic Gene Expression Oscillations

Investigation on optimization-oriented EPC method in analyzing the non-linear oscillations under multiple excitations

The optimization-oriented exponential-polynomial-closure (OEPC) method is extended and investigated to analyze stochastic nonlinear oscillators under multiple excitations, with the purpose of obtaining probabilistic solutions for the corresponding system. The presented method extends the original EPC projection procedure for solving the FPK equation by minimizing an objective function, which is defined as the spatial integration of the weighted square residual error. Using the exponential polynomial function, the parameters within it can be located by seeking the minimum of the objective function. In this paper, the novel method has been tested with four examples of strong nonlinearities raised by polynomial nonlinear terms and parametric excitations. The results provide adequate evidence that the OEPC approach delivers notably improved accuracy compared to the Gaussian closure method and demonstrates superior efficiency compared to Monte Carlo simulation. The OEPC method presents a viable alternative for investigating stochastic nonlinear oscillators.

Design Algorithmic Trading Strategies with Expert Advisor Using Linear Weighted Moving Average (LWMA) and Stochastic Oscillator Technical Indicators

Earlier this decade, the financial sector saw a paradigm change, with automated trading (AT) systems gaining popularity as essential tools for traders and investors. This research explores deeply the design and implementation of Expert Advisors (EAs) for automated financial built using a combination of the Linear Weighted Moving Average (LWMA) and Stochastic oscillator technical indicators. The EAs are built using the programming language MetaQuotes Language 4 (MLQ4) at Metatrader 4 (MT4) platform, enabling automated trade execution. It implements a machine learning genetic algorithm, trained on historical data to optimize the parameters of the LWMA and Stochastic trading rules. The core strategy relies on the LWMA to identify the overall market trend direction while the Stochastic oscillator provides additional signals for timing entry and exit points based on momentum. The EAs were coded to generate automated buy and sell signals for algorithmic trading (AT) based on a set of defined rules using thresholds for each indicators. Extensive historical backtesting using Gold (XAU/USD) currency pair across multiple timeframes from 5-minute (M5) up to 4-hour (H4) charts was conducted using 5 years of price data from 2019 to 2023 for evaluation. The goal of this study is to assess if the EAs could potentially produce consistent profits over time while minimizing drawdowns in different market conditions. The results demonstrate that the system was able to generate annual returns ranging from 3.04% up to 232.19% depending on the aggression of the timeframe settings. Meanwhile, maximum drawdowns were controlled to reasonable levels between 0.5% to 8.27% which is below 10% of potential loss throughout the backtests. An hourly timeframe configuration provided a balanced blend between strong profitability and drawdown control based on the backtest analysis. All the timeframes used for the test show positive results and the M5 timeframe is the best chosen timeframe to trade using this EAs implementation.

Evolutionary Probabilistic Analysis of Non-Smoothly Damped Stochastic Oscillator Under Modulated Random and Harmonic Excitations

This paper concerns the evolutionary transitional probability density functions (PDFs) and the mean upcrossing rates (MCRs) of responses of the non-smoothly damped stochastic oscillator under both modulated random and harmonic excitations. The damping expressed by a non-smooth function of velocity is considered in the stochastic dynamical systems. A procedure is presented by making the time-related weighted residue of the formulated Fokker–Planck–Kolmogorov (FPK) equation vanish in the weak sense. Thus, a group of stochastic ordinary differential equations regarding the undetermined parameters in the assumed solution can be formulated and solved numerically. Three cases are studied under different conditions. The achieved evolutionary transitional PDF and MCR solutions attest to the outstanding effectiveness of the presented procedure even in the tail ends of the PDF solutions. Moreover, the achieved solutions of the stochastic dynamical systems are found to have significant non-Gaussian behaviors due to the interaction of the random and harmonic excitations and the system nonlinearity. Notably, the presented procedure greatly improves the running efficiency when compared with Monte Carlo simulation.

Learning spiking neuronal networks with artificial neural networks: neural oscillations.

First-principles-based modelings have been extremely successful in providing crucial insights and predictions for complex biological functions and phenomena. However, they can be hard to build and expensive to simulate for complex living systems. On the other hand, modern data-driven methods thrive at modeling many types of high-dimensional and noisy data. Still, the training and interpretation of these data-driven models remain challenging. Here, we combine the two types of methods to model stochastic neuronal network oscillations. Specifically, we develop a class of artificial neural networks to provide faithful surrogates to the high-dimensional, nonlinear oscillatory dynamics produced by a spiking neuronal network model. Furthermore, when the training data set is enlarged within a range of parameter choices, the artificial neural networks become generalizable to these parameters, covering cases in distinctly different dynamical regimes. In all, our work opens a new avenue for modeling complex neuronal network dynamics with artificial neural networks.

Analyzing the Impact of COVID-19 on Short-Term Investment Behavior through Stochastic Oscillator Indicators

Abstract This research examines how the COVID-19 pandemic affects short-term investments, particularly focusing on the reliability of Stochastic Oscillator Indicators (SOI) used by investors. Utilizing an artificial intelligence learning prediction model, the study investigates the pandemic's impact on short-term investment strategies guided by SOI, comparing data from pre-pandemic and pandemic periods. The findings suggest that during the COVID-19 period, employing KD analysis with a nine-round turnover rate leads to higher forecast accuracy. Short-term investors tend to adopt a conservative approach, with higher turnover rates resulting in lower winning rates. Overall, the study challenges the notion that COVID-19 only affects medium and long-term investment habits, shedding light on its influence on daily investment profits and potentially increasing short-term profits for larger, conservative investors. Further research is warranted to explore the investor profile of conservative hedgers in more depth. Keywords: COVID-19, Stochastic Oscillator Indicators, Artificial Intelligence, Short-term Investors, Conservative Approach

Ultralow Glassy Thermal Conductivity and Controllable, Promising Thermoelectric Properties in Crystalline o-CsCu5S3.

We thoroughly investigated the anharmonic lattice dynamics and microscopic mechanisms of the thermal and electronic transport characteristics in orthorhombic o-CsCu5S3 at the atomic level. Taking into account the phonon energy shifts and the wave-like tunneling phonon channel, we predict an ultralow κL of 0.42 w/mK at 300 K with an extremely weak temperature dependence following ∼T-0.33. These findings agree well with experimental values along with the parallel to the Bridgman growth direction. The κL in o-CsCu5S3 is suppressed down to the amorphous limit, primarily due to the unconventional Cu-S bonding induced by the p-d hybridization antibonding state coupled with the stochastic oscillation of Cs atoms. The nonstandard temperature dependence of κL can be traced back to the critical or dominant role of wave-like tunneling of phonon contributions in thermal transport. Moreover, the p-d hybridization of Cu(3)-S bonding results in the formation of a valence band with "pudding-mold" and high-degeneracy valleys, ensuring highly efficient electron transport characteristics. By properly adjusting the carrier concentration, excellent thermoelectric performance is achieved with a maximum thermoelectric conversion efficiency of 18.4% observed at 800 K in p-type o-CsCu5S3. Our work not only elucidates the anomalous electronic and thermal transport behavior in the copper-based chalcogenide o-CsCu5S3 but also provides insights for manipulating its thermal and electronic properties for potential thermoelectric applications.

Local Lipschitz Continuity in the Initial Value and Strong Completeness for Nonlinear Stochastic Differential Equations

Recently, Hairer et al. (2015) showed that there exist stochastic differential equations (SDEs) with infinitely often differentiable and globally bounded coefficient functions whose solutions fail to be locally Lipschitz continuous in the strong L p L^p -sense with respect to the initial value for every p ∈ ( 0 , ∞ ] p\in (0,\infty ] . In this article we provide conditions on the coefficient functions of the SDE and on p ∈ ( 0 , ∞ ] p \in (0,\infty ] that are sufficient for local Lipschitz continuity in the strong L p L^p -sense with respect to the initial value and we establish explicit estimates for the local Lipschitz continuity constants. In particular, we prove local Lipschitz continuity in the initial value for several nonlinear stochastic ordinary and stochastic partial differential equations in the literature such as the stochastic van der Pol oscillator, Brownian dynamics, the Cox-Ingersoll-Ross processes and the Cahn-Hilliard-Cook equation. As an application of our estimates, we obtain strong completeness for several nonlinear SDEs.

Synchrony in Networks of Type 2 Interneurons Is More Robust to Noise with Hyperpolarizing Inhibition Compared to Shunting Inhibition in Both the Stochastic Population Oscillator and the Coupled Oscillator Regimes.

Synchronization in the gamma band (25-150 Hz) is mediated by PV+ inhibitory interneurons, and evidence is accumulating for the essential role of gamma oscillations in cognition. Oscillations can arise in inhibitory networks via synaptic interactions between individual oscillatory neurons (mean-driven) or via strong recurrent inhibition that destabilizes the stationary background firing rate in the fluctuation-driven balanced state, causing an oscillation in the population firing rate. Previous theoretical work focused on model neurons with Hodgkin's Type 1 excitability (integrators) connected by current-based synapses. Here we show that networks comprised of simple Type 2 oscillators (resonators) exhibit a supercritical Hopf bifurcation between synchrony and asynchrony and a gradual transition via cycle skipping from coupled oscillators to stochastic population oscillator (SPO), as previously shown for Type 1. We extended our analysis to homogeneous networks with conductance rather than current based synapses and found that networks with hyperpolarizing inhibitory synapses were more robust to noise than those with shunting synapses, both in the coupled oscillator and SPO regime. Assuming that reversal potentials are uniformly distributed between shunting and hyperpolarized values, as observed in one experimental study, converting synapses to purely hyperpolarizing favored synchrony in all cases, whereas conversion to purely shunting synapses made synchrony less robust except at very high conductance strengths. In mature neurons the synaptic reversal potential is controlled by chloride cotransporters that control the intracellular concentrations of chloride and bicarbonate ions, suggesting these transporters as a potential therapeutic target to enhance gamma synchrony and cognition.