Complex Model Research Articles

What can we learn when fitting a simple telegraph model to a complex gene expression model?

In experiments, the distributions of mRNA or protein numbers in single cells are often fitted to the random telegraph model which includes synthesis and decay of mRNA or protein, and switching of the gene between active and inactive states. While commonly used, this model does not describe how fluctuations are influenced by crucial biological mechanisms such as feedback regulation, non-exponential gene inactivation durations, and multiple gene activation pathways. Here we investigate the dynamical properties of four relatively complex gene expression models by fitting their steady-state mRNA or protein number distributions to the simple telegraph model. We show that despite the underlying complex biological mechanisms, the telegraph model with three effective parameters can accurately capture the steady-state gene product distributions, as well as the conditional distributions in the active gene state, of the complex models. Some effective parameters are reliable and can reflect realistic dynamic behaviors of the complex models, while others may deviate significantly from their real values in the complex models. The effective parameters can also be applied to characterize the capability for a complex model to exhibit multimodality. Using additional information such as single-cell data at multiple time points, we provide an effective method of distinguishing the complex models from the telegraph model. Furthermore, using measurements under varying experimental conditions, we show that fitting the mRNA or protein number distributions to the telegraph model may even reveal the underlying gene regulation mechanisms of the complex models. The effectiveness of these methods is confirmed by analysis of single-cell data for E. coli and mammalian cells. All these results are robust with respect to cooperative transcriptional regulation and extrinsic noise. In particular, we find that faster relaxation speed to the steady state results in more precise parameter inference under large extrinsic noise.

Optimal parameters identification for PEMFC using autonomous groups particle swarm optimization algorithm

The precise model for Polymer Electrolyte Membrane Fuel Cells (PEMFCs) is vital for simulation, control, and performance analysis of PEMFCs. It is crucial to accurately estimate the model parameters. Over the past decade, the extraction of unknown parameters of PEMFCs model is formulated as optimization problem and several meta-heuristic techniques have emerged to solve this problem. Despite the development of these techniques to tackle the problem, the slow convergence rate and susceptibility to being trapped in local minima are regarded as weaknesses of these methods. Additionally, because the PEMFC model is a nonlinear and complex model, not all optimization algorithms are suitable for solving it. This article introduces a novel approach that utilizes the Autonomous Groups Particle Swarm Optimization (AGPSO) algorithm for extracting precise values for uncertain parameters inherent in PEMFC model of 250Wstack and BCS-500W stack utilized significantly in the literature. The optimization problem's fitness function is formulated as the total squared errors (TSEs) between the voltage datasets measured and estimated. Three different versions of AGPSO algorithm are presented. Statistical analysis is performed on these three versions to assess their robustness, and the most robust version is identified. Furthermore, the performance of the most robust version is extensively tested and analyzed through a complete comparison with recent optimization algorithms findings from the updated state-of-the-art literature such as BO, QOBO, TGA, HHO and ASO. Further, a statistical analysis was carried out that ensured the reliability and robustness of the introduced AGPSO. The results highlight the efficacy and feasibility of AGPSO-based approach across all compared algorithms, demonstrating an enhancement in the accuracy of the PEMFC model. A two-phase sensitivity analysis, conducted through Monte Carlo Simulation (MCS), was employed to assess how variations in optimized parameters affect the objective function (TSEs). Furthermore, the uncertainty in the maximum power reference current is identified.

Decomposition in an extreme cold environment and associated microbiome—prediction model implications for the postmortem interval estimation

IntroductionThe accurate estimation of postmortem interval (PMI), the time between death and discovery of the body, is crucial in forensic science investigations as it impacts legal outcomes. PMI estimation in extremely cold environments becomes susceptible to errors and misinterpretations, especially with prolonged PMIs. This study addresses the lack of data on decomposition in extreme cold by providing the first overview of decomposition in such settings. Moreover, it proposes the first postmortem microbiome prediction model for PMI estimation in cold environments, applicable even when the visual decomposition is halted.MethodsThe experiment was conducted on animal models in the second-coldest region in the United States, Grand Forks, North Dakota, and covered 23 weeks, including the winter months with temperatures as low as −39°C. Random Forest analysis models were developed to estimate the PMI based either uniquely on 16s rRNA gene microbial data derived from nasal swabs or based on both microbial data and measurable environmental parameters such as snow depth and outdoor temperatures, on a total of 393 samples.ResultsAmong the six developed models, the best performing one was the complex model based on both internal and external swabs. It achieved a Mean Absolute Error (MAE) of 1.36 weeks and an R2 value of 0.91. On the other hand, the worst performing model was the minimal one that relied solely on external swabs. It had an MAE of 2.89 weeks and an R2 of 0.73. Furthermore, among the six developed models, the commonly identified predictors across at least five out of six models included the following genera: Psychrobacter (ASV1925 and ASV1929), Carnobacterium (ASV2872) and Pseudomonas (ASV1863).DiscussionThe outcome of this research provides the first microbial model able to predict PMI with an accuracy of 9.52 days over a six-month period of extreme winter conditions.

Low complexity model predictive current control for dual three-phase permanent magnet synchronous motor with extended control set and duty cycle modulation

Low complexity model predictive current control for dual three-phase permanent magnet synchronous motor with extended control set and duty cycle modulation

The adsorption of U(VI) on chlorite: batch, modeling and XPS study

Abstract A mechanistic modelling of the adsorption processes onto individual minerals presenting in the near- and far-fields can greatly enhance the credibility of long-term safety assessments of granite-based geological repositories. In this study, the titration and U(VI) adsorption characteristics of chlorite, one of the major minerals of rock fractures, have been studied. Potentiometric titration curves at two ionic strengths (0.1 and 0.4 mol/L NaCl) are successfully interpreted by considering protonation/deprotonation reactions on generic edge sites (≡SOH) in the framework of a non-electrostatic surface complexation model (SCM). The adsorption of U(VI) on chlorite was reached after 24 h, the adsorption kinetics can be described by a pseudo-second-order model. A non-electrostatic SCM with three surface complexes (≡SOUO2 +, ≡SO(UO2)3(OH)5 and ≡SO(UO2)3(OH)7 2−) was set up based on pH edges of U(VI) at adsorption equilibrium in the absence of CO2. Additional, experimental data measured as a function of U(VI) concentration, solid-to-liquid ratio and carbonate concentration were well reproduced by the proposed model. Finally, parallel experiments were conducted using X-ray photoelectron spectroscopy (XPS) to analyze the variation of U(VI) surface species speciation at different pH values. The good agreement between SCM prediction and XPS analysis demonstrates the reliability of the model in predicting and quantifying the radionuclides retention by chlorite.

Innovative control strategy for flood mitigation through a combination of barrage management on impounded rivers and polders

The partially catastrophic effects of large floods, such as the events of 2002 and 2013 in Germany and Austria for example, clearly show the vulnerability of settlement structures along large rivers. In the case of impounded rivers with run-of-river hydropower plants, the main question is whether a reduction of floods can be achieved with flood-adapted, intelligent control of barrages - to date, the operational objective has been the safe discharge of floodwater; targeted reduction is currently an unoccupied field due to its complexity. Specifically, the interaction with the operation of a polder for flood retention is of special interest, as polders are a much-discussed and effective element of flood protection, especially at higher discharges, that directly influences the hydrograph shape. Extensive analyses and sensitivity investigations of a multitude of parameters and measured values, using a complex model system, are needed in order to investigate the reduction potential of the named technical flood protection measures and the development of control strategies relevant to practice. It is essential to base the developed controlling strategies on operationally available data, as this is the only way to make the determined reductions relevant for practical operation.

Optimal charging for lithium-ion batteries to avoid lithium plating based on ultrasound-assisted diagnosis and model predictive control

Lithium plating in lithium-ion batteries for electric vehicles, occurring due to low-temperature or high-rate charging, is a significant factor impacting safety and service life. To address this issue, a novel adaptive charging approach is proposed, combining ultrasound-assisted diagnosis and model predictive control (MPC). In the method, a discrete state-space electrochemical model is used to describe the dynamic characteristics of the battery, and a model predictive controller (MPC) is utilized to optimize the charging current to avoid lithium plating. Considering that factors such as battery performance degradation and variable working temperature affect the battery model's judgment of lithium plating, an ultrasound-assisted diagnosis method is used to determine the critical point of lithium plating. The effectiveness of the method is validated through low-temperature charging and cycle aging experiments. The results indicate that without complex model parameter calibration in different temperatures, the new charging method not only has a higher charging speed than constant current charging, but also can effectively suppress the occurrence of lithium plating on the negative electrode of the battery. The method is expected to be applied in electrochemical energy storage systems to enhance safety and service life.

Mechanism of Evolution of Shock Wave of Muzzle Jet under Initial Interference and Its Simplified Model

Large-caliber and long-barrel weapons are important experimental devices for exploring the impact resistance and reliability of warheads. The force of impact of the muzzle jet has a significant influence on the overload resistance of the warhead and surrounding devices. The mechanism of motion of the body inside the tube cannot be ignored owing to the high kinetic energy at the muzzle. In this study, we designed the relevant experiment and a simulation model to analyze the structural characteristics and mechanism of evolution of the shock wave and the vortex structure in a muzzle jet. The aim was to examine the evolution of the shock wave with initial jet-induced interference. And we established three other simulation models to compare the similarities and differences between the results of the models. The results showed that, in the original complex model, the initial jet restricted the free expansion of the muzzle jet, and this led to many shock–shock collisions that retarded the development of the shock waves. Multiple reflected shock waves were thus formed under a high local pressure that distorted the shock structure, while the structure of the shock wave in the simplified models was clear and simple. The parameters of motion of the body changed by a little when the initial jet-induced interference was ignored. The difference in values of the strongest impact force measured at monitoring points far from the muzzle was small, with an error of about 2%, such that the simplified model without the initial jet could be used in place of the original complex model. The other simplified models yielded significant differences. Our results provide an important theoretical basis for further research on the muzzle jet and its applications in engineering.

Modelling Wear Phenomena Specific to Mixer Blades in Concrete Production Plants

In the cement concrete manufacturing industry, mixers are critical pieces of equipment that play an essential role. Mixers ensure, by mechanically mixing the materials that make up the concrete, the homogeneity of the mixture. Since the active elements of the mixer in the concrete industry—the mixing blades—come into permanent contact with the mineral aggregates in the mixture formed by water and cement, they are permanently subjected to a strong abrasive–erosive wear process. The authors of this article were concerned with the establishment of tribological models for studying the wear of mixing blades, in order to identify the influence of their constructive parameters on the wear intensity. A complex model (Kraghelsky–Nepomnyashchi model) was adopted for the study. The modeling results revealed that the wear intensity decreases with an increasing blade angle of attack and increases linearly with increasing speed, as well as with an increasing friction coefficient. The modeling results confirm that the wear intensity is lowest when the mixing blade is inclined at a 60° angle, while the highest value is recorded for 30°. By identifying the angle at which the greatest wear of blades occurs, interventions can be made in the design of a more durable mixer (with the optimal installation angle of the mixer blades), thus requiring fewer corrective maintenance interventions. Based on these findings, we conclude that the complex model used in the experiment can provide a convenient and efficient tool for the study of erosive–abrasive phenomena.

Forecasting Total and Type-Specific Non-Residential Building Construction Spending: The Case Study of the United States and Lessons Learned

Forecasting construction spending is important for civil engineering practitioners to make business decisions. Currently, the main body of forecasting literature pertains exclusively to aggregate construction investment, such as total construction spending (TTLCON), private construction spending, or residential construction spending. But type-specific construction spending, such as that for education, healthcare, and religion, had yet to be explored using forecasting techniques. This case study presents a viable procedure by which aggregate and type-specific non-residential construction can be forecasted. The procedure that involves the use of the Granger causality test and the Vector Autoregression (VAR) model proved to be able to provide an accurate forecast pre-COVID-19, with some accuracy even during the COVID-19 pandemic period. Lessons learned include the following: (1) effort should be diverted towards model interpretation, as the impulse–response trial yields results conforming to current well-established empirical evidence; (2) a type-specific approach should be adopted when analyzing construction spending, as different types of construction spending react differently to potential indicators; and (3) complex models incorporating multiple indicators should be used to generate a forecast, as a complex model has a higher chance of containing parameters explanatory of the target variable’s features during the testing period.

Open‐source stand‐alone version of atmospheric model Aeolus 2.0 software

AbstractIn this discourse, we present the unveiling of an open‐source software package designed to facilitate engagement with the atmospheric model, Aeolus 2.0. This particular iteration stands as a self‐contained model of intermediate complexity. The model's dynamical core is underpinned by a multi‐layer pseudo‐spectral moist‐convective Thermal Rotating Shallow Water (mcTRSW) model. The pseudo‐spectral problem‐solving tasks are handled by the Dedalus algorithm, acknowledged for its spin‐weighted spherical harmonics. The model captures the temporal and spatial evolution of vertically integrated potential temperature, thickness, water vapour, precipitation, and the intricate influence of bottom topography. It comprehensively characterizes velocity fields in both the lower and upper troposphere, employing resolutions spanning a spectrum from the smooth to the coarse, enabling the exploration of a wide range of dynamic phenomena with varying levels of detail and precision.

Assessing Residential Building Energy Efficiency Using Evolutionary Dendritic Neural Regression

Assessing building energy consumption is of paramount significance in sustainability and energy efficiency (EE) studies. The development of an accurate EE prediction model is pivotal for optimizing energy resources and facilitating effective building planning. Traditional physical modeling approaches are encumbered by high complexity and protracted modeling cycles. In this paper, we introduce a novel evolutionary dendritic neural regression (EDNR) model tailored to forecasting residential building EE. Acknowledging the vast landscape and complexity of the EDNR weight space, coupled with the inherent susceptibility of traditional optimization algorithms to local optima, we propose a complex network-guided strategy-based differential evolution algorithm for training the EDNR model. This strategy adeptly strikes a balance between exploration and exploitation during the search process, significantly enhancing the predictive and generalization capacities of EDNR. To our knowledge, this study represents the inaugural application of dendritic neural regression in real-world prediction scenarios. Extensive experimental findings demonstrate the efficacy of EDNR in accurately predicting building EE with commendable performance. Furthermore, the results of two nonparametric statistical tests affirm the validity and stability of EDNR. Consequently, our proposed methodology exhibits high potential and competitiveness in machine learning applications within the energy domain.

A data-driven soft sensor model for coal-fired boiler SO2 concentration prediction with non-stationary characteristic

Environmental issues have received significant global attention, and achieving ultra-low emission has become a crucial goal for thermal power plant. Pollutant prediction is essential to achieving ultra-low emission control. Due to the frequent adjustment of operating conditions, the coal-fired power generation process is a typical non-stationary process with complex changes along the time direction. A single model cannot effectively portray the complex non-stationary characteristics and model mismatch may occur in the prediction, which brings new challenges for modeling coal-fired SO2 emission. Therefore, the condition-driven category boosting (CatBoost) soft sensor model is proposed for real-time prediction of SO2 concentration. First, the thermal process time series is rearranged into different data slices. These data slices vary along the direction of the condition indicator, which can characterize the process characteristics on different slices. Second, the load-based sequential condition division (LSCD) algorithm is designed to realize the division of boiler operation process. The characteristics of process are effectively captured by variational auto-encoder (VAE), and the data slices with similar process characteristics are merged into the same mode. Non-stationary process along the time direction is reorganized into different condition modes along the load direction. Finally, the high-resolution local CatBoost models under different modes are constructed to achieve fine-grained prediction of SO2 concentration. The effectiveness of the proposed condition-driven model is verified by an industrial example of 1000 MW coal-fired boiler. The prediction results show that the proposed model can effectively divide the operation conditions and achieve accurate prediction of SO2 concentration. In the typical models in SO2 predicting, the proposed model has better performance with a determination coefficient of 0.92.

Xai-driven knowledge distillation of large language models for efficient deployment on low-resource devices

Large Language Models (LLMs) are characterized by their inherent memory inefficiency and compute-intensive nature, making them impractical to run on low-resource devices and hindering their applicability in edge AI contexts. To address this issue, Knowledge Distillation approaches have been adopted to transfer knowledge from a complex model, referred to as the teacher, to a more compact, computationally efficient one, known as the student. The aim is to retain the performance of the original model while substantially reducing computational requirements. However, traditional knowledge distillation methods may struggle to effectively transfer crucial explainable knowledge from an LLM teacher to the student, potentially leading to explanation inconsistencies and decreased performance. This paper presents DiXtill, a method based on a novel approach to distilling knowledge from LLMs into lightweight neural architectures. The main idea is to leverage local explanations provided by an eXplainable Artificial Intelligence (XAI) method to guide the cross-architecture distillation of a teacher LLM into a self-explainable student, specifically a bi-directional LSTM network.Experimental results show that our XAI-driven distillation method allows the teacher explanations to be effectively transferred to the student, resulting in better agreement compared to classical distillation methods,thus enhancing the student interpretability. Furthermore, it enables the student to achieve comparable performance to the teacher LLM while also delivering a significantly higher compression ratio and speedup compared to other techniques such as post-training quantization and pruning, which paves the way for more efficient and sustainable edge AI applications

Acoustic wave propagation and scattering in visco-acoustic medium: Integral equation representation and De Wolf approximation

A visco-acoustic medium is an approximate representation of the absorption and attenuation characteristics of the actual earth medium, which will cause energy attenuation and velocity dispersion of seismic waves. The propagation law of scattered waves in viscoelastic media can be revealed through seismic wave forward simulation. However, the numerical simulation of scattered waves in a visco-acoustic medium using the De Wolf approximation method based on the Lippmann-Schwingr (L-S) equation has not been studied. Therefore, based on the Futterman dispersion relation, the mathematical expression of the integral equation of acoustic wave propagation and scattering in the visco-acoustic medium is derived. We combine the De Wolf approximation with the quality factor Q. The thin slab approximation and screen approximation methods are two realizations of the De Wolf approximation. The thin slab approximation and the screen approximation continuation operator in the viscous-acoustic medium are constructed and applied to the numerical simulation of the scattered wave field. The research results of the concave model and complex model indicate that due to the influence of medium viscosity, the energy of the deep reflected waves is weaker in the forward modeling records of the thin slab approximation method and screen approximation method, and the dominant frequency of seismic waves moves towards the low-frequency direction; Compared with the finite difference results, they only calculate one reflection, and there are no multiple wave signals in the seismic records. Finally, We discuss the thin slab approximation and the screen approximation method for detail around the division of the thickness of the thin slab, the selection of the reference frequency, and the non-uniformity of the medium.

Insights into Bitcoin and energy nexus. A Bitcoin price prediction in bull and bear markets using a complex meta model and SQL analytical functions

AbstractCryptocurrencies are in the center of attention of investors, public authorities and researchers, but the interest has shifted from purely financial aspects regarding the way of trading, lack of regulation and supervision of transactions, volatility, correlation with other assets to aspects related to sustainability taking in account the high energy consumption generated by the mining process and the impact on environmental pollution. Bitcoin was chosen for the research considering the dominance that this financial asset has on the cryptocurrency market and its position as alpha currency.The article focuses on the relationship between Bitcoin transactions and energy consumption, for period 1st January 2019—31st of May 2022, this interval having significant price movements. The authors made a prediction of the Bitcoin price using a complex meta-model and SQL analytical functions. The analysis is based on 15 fundamental variables in order to forecast the price: Bitcoin data (prices and volume), electricity price and traded quantity on day-ahead market (DAM), gas price and traded quantity on DAM, inflation in EU, EU-ETS emissions certificates and oil prices. The study reveals the importance of the relationship Bitcoin—energy—carbon emissions, elements that capture the impact of the mining process on the environment from the perspective of energy consumption. Investors on the Bitcoin market must be aware not only of the importance of financial aspects on the price of cryptocurrencies (inflation, demand, offer), but also of other elements related to the evolution of energy prices (electricity, oil, gas, renewable energy) and the evolution of emissions certificates prices. Considering the promotion of the principles of sustainable development on the capital market, portfolio investors have become increasingly attentive to the social and environmental performance of financial assets. This study aims to make financial market players aware of the non-financial implications of their transactions. In addition, the energy transition and the reconfiguration of the energy mix are elements of impact on the cryptocurrency market through the technical levers involved in the mining process.

Validation of the added mass effect in the narrow gaps of nuclear reactor pressure vessels

Nuclear reactor pressure vessels (RPVs) must be robust to external environmental excitations such as seismic loads. Precise numerical models that predict the dynamic responses to external loads are crucial for evaluating the safety of RPVs. Notably, in RPVs submerged in reactor coolant, it is necessary to examine the added mass effect of the fluid via fluid-structure interaction (FSI) analysis, employing either an analytical approach or a numerical analysis. The present study focuses on modeling and analyzing the added mass effect in the narrow gaps associated with the dense structural layout in the reactor. In this context, this paper validates analytical and numerical models that accurately describe the added mass effect for two cases: (i) simple concentric cylinders with a narrow gap filled with fluid and (ii) a complex small-scale RPV with narrow gaps also filled with fluid. Initially, the analytical model, employing Lagrange's equation of motion and velocity potential, and the numerical model, utilizing FE modeling in acoustic FSI through ANSYS, were validated through experimental modal testing for the added mass effect in the narrow gap between simple concentric cylinders. The analytical model for the concentric cylinders indicates that the added mass diverges to infinity as the gap approaches zero, which should be examined carefully. Through experiments for the concentric cylinders, the analytical and FEM-based added mass effects were validated with a natural frequency error of 3 %. Subsequently, based on the results for the concentric cylinders, a complex numerical model of the small-scale reactor with complex boundary conditions was developed and cross-validated through corresponding experimental modal testing of the small-scale RPV. The added mass model for the narrow gaps in the RPV was validated by substantial agreement of eight representative modes, as demonstrated by a 5 % natural frequency error.

Impact of Clinical Characteristics and Biomarkers on Asthma Impairment and Risk Questionnaire Exacerbation Prediction Ability

Complex models combining impairment-based control assessments with clinical characteristics and biomarkers have been developed to predict asthma exacerbations. The composite Asthma Impairment and Risk Questionnaire (AIRQ) with adjustments for demographics (age, sex, race, body mass index [BMI]) predicts 12-month exacerbation occurrence similarly to these more complex models. To examine whether AIRQ exacerbation prediction is enhanced when models are adjusted for a wider range of clinical characteristics and biomarkers. Patients aged ≥12 years completed monthly online surveys regarding exacerbation-related oral corticosteroid use, emergency-department/urgent-care visits, and hospitalizations. Univariate logistic regressions to predict exacerbations were performed with sociodemographics, comorbidities, exacerbation history, lung function, blood eosinophils, immunoglobulin E, and fractional exhaled nitric oxide. Significant (P≤0.05) variables were included in multivariable logistic regressions with and without AIRQ control categories to predict 12-month exacerbations (log odds ratio [OR], 95% Wald confidence interval [CI]). Model performances were compared. Over 12 months, 1070 patients (70% female; mean[SD] age 43.9[19.4] years; 22% non-White; BMI[SD] 30.6[8.7]) completed ≥1 survey (mean[SD] 10.5[2.8]). In the multivariable analysis, AIRQ control category adjusted for significant clinical characteristics and biomarkers was predictive of ≥1 exacerbation: OR(95%CI) not well-controlled vs well-controlled: 1.93(1.41-2.62), very poorly controlled vs well-controlled: 3.81(2.65-5.47). Receiver operating characteristic area under the curve for this more complex model of exacerbation prediction (AUC=0.72) did not differ from AIRQ (AUC=0.70). Models with AIRQ performed better than those without AIRQ (AUC=0.67, P<0.05). Costly and time-consuming complex modeling with clinical characteristics and biomarkers does not enhance the strong exacerbation prediction ability of AIRQ.

Comparing flows of FENE-P, sPTT, and Giesekus model fluids in a helical static mixer

Helical static mixers are used widely for mixing of non-Newtonian fluid flows in the laminar regime. We study flows of three viscoelastic constitutive models (sPTT, FENE-P, and Giesekus) in the helical static mixer using computational fluid dynamics. These three models have similarities in steady viscometric flows in that they all exhibit shear thinning and their planar extensional viscosities can be matched, but their responses can differ in complex geometries. We observe flow distribution asymmetries at the element intersections for all three models, which hinders the mixing performance of the device. These have previously been observed with the constant shear viscosity FENE-CR model. The asymmetry behaves similarly between the sPTT and Giesekus models, however the FENE-P model behaves in a distinct manner; beyond a critical degree of elasticity, the asymmetry sharply changes direction. This was also observed previously with the FENE-CR model. These results suggest that shear thinning and second-normal stress differences (present in the Giesekus model) do not significantly influence mixing performance in the range of conditions studied. We show that increasing the aspect (length/diameter) ratio of the mixer elements mitigates the poor mixing caused by elasticity. Overall, this study provides insight into the behaviour of these well-used constitutive models in complex, industrially-relevant flows.

Dynamical bifurcation of a stochastic Holling-II predator–prey model with infinite distributed delays

This paper serves as a continuation and expansion of the previous achievement by B. Han and D. Jiang in their article (Han and Jiang, 2024). Our initial step involves transforming the more complex stochastic Holling-II model featuring a stronger kernel into a simplified yet degenerate stochastic system composed of five interconnected equations. For the deterministic component of this model, we delve into an extensive examination of the local asymptotic stability of its positive equilibrium state. Subsequently, for the stochastic model, we derive critical conditions that determine the thresholds for exponential extinction and persistence of both predator and prey populations. Importantly, our findings not only encompass scenarios where there are no stochastic disturbances but also shed light on how environmental noise impacts the population dynamics within the predator–prey system. Through the exploration of the homologous Fokker–Planck equations, we present approximate representations characterizing the probability density function of the stochastic predator–prey model. To substantiate these theoretical advancements, several illustrative examples are provided, offering numerical elucidations of our proposed results and emphasizing the profound effects of stochastic noises and some important parameters on the behaviors of the stochastic model.