Set Of Parameters Research Articles

Analysis and Optimization of Multi-Physical Field Coupling in Boom Flow Channel of Excavator Multiway Valves

The multiway valve is the core control element of the hydraulic system in construction machinery, such as excavators. Its complex internal structure, especially the flow channels, significantly impacts the machine’s efficiency and reliability. This study focuses on the boom flow channel of excavator multiway valves and establishes a multi-physical field coupling simulation model. We propose six key flow channel structural parameters and analyze changes in the valve’s flow field, temperature field, and structural field using orthogonal test simulation data. The range analysis method identifies the primary and secondary influences of structural parameters on pressure loss, temperature, stress, and strain. A multi-objective optimization model was developed using a neural network and the Non-dominated Sorting Genetic Algorithm II(NSGA-II), with pressure loss and maximum stress as the optimization objectives. The Pareto front solution set for key flow channel parameters was calculated. The optimization results showed a 9.0% reduction in pressure loss and a 40.7% reduction in maximum stress. A test bench verified the simulation model, achieving prediction accuracies of 94.8% for pressure loss in the inlet area and 92.3% in the return area. This method can provide a reference for the optimal design of the dynamic characteristics of high-pressure multiway valves.

Brain Image Segmentation for Ultrascale Neuron Reconstruction via an Adaptive Dual-Task Learning Network.

Accurate morphological reconstruction of neurons in whole brain images is critical for brain science research. However, due to the wide range of whole brain imaging, uneven staining, and optical system fluctuations, there are significant differences in image properties between different regions of the ultrascale brain image, such as dramatically varying voxel intensities and inhomogeneous distribution of background noise, posing an enormous challenge to neuron reconstruction from whole brain images. In this paper, we propose an adaptive dual-task learning network (ADTL-Net) to quickly and accurately extract neuronal structures from ultrascale brain images. Specifically, this framework includes an External Features Classifier (EFC) and a Parameter Adaptive Segmentation Decoder (PASD), which share the same Multi-Scale Feature Encoder (MSFE). MSFE introduces an attention module named Channel Space Fusion Module (CSFM) to extract structure and intensity distribution features of neurons at different scales for addressing the problem of anisotropy in 3D space. Then, EFC is designed to classify these feature maps based on external features, such as foreground intensity distributions and image smoothness, and select specific PASD parameters to decode them of different classes to obtain accurate segmentation results. PASD contains multiple sets of parameters trained by different representative complex signal-to-noise distribution image blocks to handle various images more robustly. Experimental results prove that compared with other advanced segmentation methods for neuron reconstruction, the proposed method achieves state-of-the-art results in the task of neuron reconstruction from ultrascale brain images, with an improvement of about 49% in speed and 12% in F1 score.

Adaptive Formation Tracking Control of Multiple Vertical Takeoff and Landing UAVs With Bearing-Only Measurements.

This article studies the leader-following formation tracking control problem of multiple vertical takeoff and landing (VTOL) unmanned aerial vehicles (UAVs) subject to uncertain parameters, in which the target formation configuration is defined by using the interneighbors' bearing vectors. An adaptive formation control algorithm with bearing-only measurements is proposed under a hierarchical control framework. More specifically, a saturated adaptive distributed control force is developed in the position loop with bearing-only measurements. Since the bearing vectors with respect to the neighbors can be directly measured by low-cost onboard cameras, the proposed formation algorithm can be implemented without interagent communication. Subsequently, in the attitude loop, an adaptive hybrid control scheme via two modified Rodrigues parameters (MRPs) sets is proposed, which achieves the command attitude tracking globally and also avoids the unwinding problem of MRPs. Based on the Lyapunov stability analysis and hybrid theory, we prove that the overall closed-loop error system is globally asymptotically stable. Finally, we provide a numerical example to demonstrate the effectiveness of the proposed control algorithm.

Schrödinger equation as a confluent Heun equation

This article deals with two classes of quasi-exactly solvable (QES) trigonometric potentials for which the one-dimensional Schrödinger equation reduces to a confluent Heun equation (CHE) where the independent variable takes only finite values. Power series for the CHE are used to get polynomial and nonpolynomial eigenfunctions. Polynomials occur only for special sets of parameters and characterize the quasi-exact solvability. Nonpolynomial solutions occur for all admissible values of the parameters (even for values which give polynomials), and are bounded and convergent in the entire range of the independent variable. Moreover, throughout the article we examine other QES trigonometric and hyperbolic potentials. In all cases, for a polynomial solution there is a convergent nonpolynomial solution.

Cryptographic Engineering a Fast and Efficient SIKE in FPGA

Recent attacks have shown that SIKE is not secure and should not be used in its current state. However, this work was completed before these attacks were discovered and might be beneficial to other cryptosystems such as SQISign. The primary downside of SIKE is its performance. However, this work achieves new SIKE speed records even using less resources than the state-of-the-art. Our approach entails designing and optimizing a new field multiplier, SIKE-optimized Keccak unit, and high-level controller. On a Xilinx Virtex-7 FPGA, this architecture performs the NIST Level 1 SIKE scheme key encapsulation and key decapsulation functions in 2.23 and 2.39 ms, respectively. The combined key encapsulation and decapsulation time is 4.62 ms, which outperforms the next best Virtex-7 implementation by nearly 2 ms. Our implementation achieves speed records for the NIST Level 1, 2, and 3 parameter sets. Only our NIST Level 5 parameter set was beat by an all-out performance implementation. Our implementations also efficiently utilize the FPGA resources, achieving new records in area-time product metrics for all parameter sets. Overall, this work continues to push the bar for accelerating SIKE computations to make a stronger case for SIKE standardization.

Comparison of photodynamic therapy with two different parameters combined with subconjunctival injection of bevacizumab for corneal neovascularization

BackgroundTo the best of our knowledge, no studies have been performed to determine the optimal parameters of photodynamic therapy (PDT) combined with subconjunctival injection of bevacizumab for corneal neovascularization. This study aimed to compare the effect of photodynamic therapy with two different sets of parameters combined with subconjunctival injection of bevacizumab for corneal neovascularization. MethodsPatients with stable corneal neovascularization (CNV) unresponsive to conventional treatment (topical steroid) were included in this study. Patients were divided into two groups, receiving PDT with two different sets of parameters (group 1 receiving fluence of 50 J/cm2 at 15 min after intravenous injection of verteporfin with, group 2 receiving fluence of 150 J/cm2 at 60 min after intravenous injection of verteporfin with). Subconjunctival injection of bevacizumab was performed immediately after PDT. All patients were followed for 6 months. Best-corrected visual acuity and intraocular pressure were evaluated, and slit-lamp biomicroscopy as well as digital photography were performed. Average diameter and cumulative length of corneal neovascular were measured to evaluate the corneal neovascularization. ResultsSeventeen patients (20 eyes) were included in this study. At the last visit, the vision was improved in 12 eyes (60 %), steady in 4 eyes (20 %) and worsen in 4 eyes (20 %). The intraocular pressure (IOP) of all patients remained in normal range. A significant decrease in corneal neovascularization was showed in all the eyes after treatment. At 6 months after the combined treatment, the average diameter and cumulative length of vessels significantly decreased to 0.041 ± 0.023 mm (P < 0.05) and 18.78 ± 17.73 mm (P < 0.05), respectively, compared with the pretreatment data (0.062 ± 0.015 mm, 31.48 ± 18.21 mm). The reduction was more remarkable in group 2 compared to group 1.In group 1, the average diameter was 0.062 ± 0.013mm before and 0.056 ± 0.017mm after, the cumulative length of vessels was 38.66 ± 22.55mm before and 31.21 ± 17.30 after. In group 2, the date were 0.061 ± 0.016mm before and 0.029 ± 0.020mm after, 25.60 ± 8.95 mm before and 8.61 ± 8.26 mm. The reported complications included epithelial defect in four eyes, small white filaments in two eyes and corneal epithelial erosion in two eyes. ConclusionThe PDT combined with subconjunctival injection of bevacizumab was effective for the chronic corneal neovascularization. A more promising treatment outcome was observed when PDT was performed at 60 min after intravenous injection of verteporfin with fluence of 150 J/cm2. No serious complications or systemic events were observed throughout the follow-up period.

Stability analysis and vibration suppression in an overhung rotor system using active magnetic damper

The present work demonstrates the effectiveness of an active magnetic damper (AMD) in improving the vibration characteristics of an overhung rotor system (ORS) considering the effects of synchronous mass-unbalance, rotor bow, and viscous internal damping. A finite element-based rotordynamic analysis has been conducted to evaluate the system response using state-space formulation. MATLAB codes are developed for the numerical implementation of the rotordynamic model pertaining to the flexible ORS integrated with an AMD consisting of three parallel feedback loops. The internal damping is found to reduce the vibration amplitudes at the bearing and disk locations. However, it leads to system instability in the absence of AMD beyond the first critical speed (670 RPM) which is indicated by the change in the real part of eigenvalues. Under these circumstances, the use of AMD causes a remarkable improvement and the system stabilizes for almost the entire speed range considered here, 320–10,000 RPM. In addition, the AMD causes a maximum reduction of 95.8%, 96.5%, and 83.3% in the vibration amplitudes at the locations of Bearing 1, Bearing 2, and the overhung disk, respectively. Using an appropriate set of AMD parameters, the system characteristics can be altered effectively as per the requirement.

Histology-driven hypofractionated radiation therapy schemes for early-stage lung adenocarcinoma and squamous cell carcinoma

Background and PurposeHistology was found to be an important prognostic factor for local tumor control probability (TCP) after stereotactic body radiotherapy (SBRT) of early-stage non-small-cell lung cancer (NSCLC). A histology-driven SBRT approach has not been explored in routine clinical practice and histology-dependent fractionation schemes remain unknown. Here, we analyzed pooled histologic TCP data as a function of biologically effective dose (BED) to determine histology-driven fractionation schemes for SBRT and hypofractionated radiotherapy of two predominant early-stage NSCLC histologic subtypes adenocarcinoma (ADC) and squamous cell carcinoma (SCC). Material and MethodsThe least-χ2 method was used to fit the collected histologic TCP data of 8510 early-stage NSCLC patients to determine parameters for a well-developed radiobiological model per the Hypofractionated Treatment Effects in the Clinic (HyTEC) initiative. ResultsA fit to the histologic TCP data yielded independent radiobiological parameter sets for radiotherapy of early-stage lung ADC and SCC. TCP increases steeply with BED and reaches an asymptotic maximal plateau, allowing us to determine model-independent optimal fractionation schemes of least doses in 1–30 fractions to achieve maximal tumor control for early-stage lung ADC and SCC, e.g., 30, 44, 48, and 51 Gy for ADC, and 32, 48, 54, and 58 Gy for SCC in 1, 3, 4, and 5 fractions, respectively. ConclusionWe presented the first determination of histology-dependent radiobiological parameters and model-independent histology-driven optimal SBRT and hypofractionated radiation therapy schemes for early-stage lung ADC and SCC. SCC requires substantially higher radiation doses to maximize tumor control than ADC, plausibly attributed to tumor genetic diversity and microenvironment. The determined optimal SBRT schemes agree well with clinical practice for early-stage lung ADC. These proposed optimal fractionation schemes provide first insights for histology-based personalized radiotherapy of two predominant early-stage NSCLC subtypes ADC and SCC, which require further validation with large-scale histologic TCP data.

Influence of contour processing parameters on porosity, surface roughness, and fatigue life in laser powder bed Al-10Si-0.4Mg

Additive manufacturing (AM) enables fabrication of net-shape components with high geometric complexity, however mechanical properties of parts with as-fabricated surfaces are limited by surface roughness and subsurface porosity that may initiate fatigue cracks. This study aims to improve the utility of parts with as-fabricated surfaces by quantifying processing-surface condition-fatigue performance relationships, optimizing surface contour parameters for fatigue performance, and investigating the application of surface profilometry as a non-destructive quality control method. Eleven contour parameter sets of varying energy densities were produced in three classifications: no contour passes, single contour passes, and contours with secondary healing passes. Surface roughness was evaluated using line scan profilometry and subsurface porosity by optical microscopy. Contouring reduced the average surface roughness from Ra ≅ 25 μm to Ra ≅ 5 μm, and the layer of subsurface porosity introduced by this process could be partially eliminated by a secondary healing pass. One set of processing conditions from each contour class was selected for fatigue studies (R = -1), and their results were compared with the fatigue data from machined and polished specimens to evaluate the relative influence of surface condition. Relative to machined and polished specimens, fatigue lives are approximately five times lower for contoured specimens (with and without a healing pass) and twenty times lower for non-contoured specimens at equivalent stress levels up to 107 cycles to failure. Fractographic measurements of initial defect √area of all specimens reveal that fatigue behavior is well characterized by stress intensity factor amplitude across all surface conditions. An extreme value statistical method is developed using profilometry data to predict S-N curves, and it is concluded that non-destructive surface roughness measurements may be suitable for estimating the fatigue lives of components with as-fabricated surfaces as a rapid method for quality control.

Confidence Intervals for Parameters of Unobserved Events

Consider a finite sample from an unknown distribution over a countable alphabet. Unobserved events are alphabet symbols which do not appear in the sample. Estimating the probabilities of unobserved events is a basic problem in statistics and related fields, which was extensively studied in the context of point estimation. In this work we introduce a novel interval estimation scheme for unobserved events. Our proposed framework applies selective inference, as we construct confidence intervals (CIs) for the desired set of parameters. Interestingly, we show that obtained CIs are dimension-free, as they do not grow with the alphabet size. Further, we show that these CIs are (almost) tight, in the sense that they cannot be further improved without violating the prescribed coverage rate. We demonstrate the performance of our proposed scheme in synthetic and real-world experiments, showing a significant improvement over the alternatives. Finally, we apply our proposed scheme to large alphabet modeling. We introduce a novel simultaneous CI scheme for large alphabet distributions which outperforms currently known methods while maintaining the prescribed coverage rate. Supplementary materials for this article are available online including a standardized description of the materials available for reproducing the work.

Modelling of beer sensory staleness based on flavour instability parameters

Why was the work done: The deterioration of the flavour of fresh beer is challenging for the brewing industry. Despite extensive research on flavour instability, the focus has centred on a limited set of parameters, rather than taking a broader approach.&#x0D; How was the work done: in this study, the intent was to produce a flavour stable beer. Using a low kilning temperature, malt of low staling potential was used in combination with best brewing practice to produce three batches of unpasteurised top fermented pale beers at a pilot scale. Forty-three markers were analysed in the fresh and aged beers (30°C for 15, 30, 60 and 90 days). Staleness was evaluated by a trained sensory panel and multivariate data analysis was used to explore how the markers contribute to staleness.&#x0D; What are the main findings: Repeatability was achieved between replicate brews and, subsequently, staling. Polyphenols, haze, total reactive antioxidant potential (TRAP), iso-α-acids, colour, furfural, 2-methylpropanal and 2-methylbutanal showed a strong correlation with staleness. Staleness doubled after 60 days of storage at 30°C, despite volatile aldehydes remaining below their sensory thresholds, implying a synergistic effect of carbonyls contributing to staleness. A Partial Least Square (PLS) model was established, modelling the sensory staleness from 2-methylpropanal, furfural, TRAP and the trans-/cis-iso-α-acids ratio.&#x0D; Why is the work important: The staling phenomena could be reproduced in beers from parallel brewing trials with only minor variations. The four parameters in PLS modelling indicate that beer staling involves a combination of oxidative and non-oxidative pathways.

Ultrasonic penetration method for weld root crack in orthotropic steel decks: differentiation and quantitative recognition

Weld root crack represents a significant concern in terms of fatigue on orthotropic steel decks (OSDs). This study presents a crack detection method based on ultrasonic penetration signals, to effectively distinguish and quantify cracks in decks. Firstly, based on the principles of sound diffusion and the structural characteristics of OSDs, the parameters were established. Then, the propagation mechanism of ultrasonic waves in decks containing cracks was investigated by finite element analysis. The variations in received signal intensity caused by root-deck and root-weld crack parameters were analyzed and the methods for distinguishing between crack types and determining characteristics were proposed. Finally, experimental tests were conducted on weld root cracks to validate the feasibility of the detection method. The research findings demonstrate that the selected detection parameters adequately meet the requirements for crack detection. By utilizing fitting functions between the transmission signals from two sets of detection parameters and the projected crack length, the method achieves accurate identification of crack length and angle, with an error rate of less than 10%.

A creep/recovery model of dry fiber fabric during compaction considering temperature and in‐plane tension

AbstractIn the manufacturing of fiber‐reinforced composite materials, the preforming stage of dry fiber fabric entails compaction operations carried out under constant pressure, a specific preforming temperature, and in‐plane tension. Throughout this process, permanent deformation and creep/recovery behavior are observed in the fabric, correlating with factors such as time, sustained pressure, temperature, and in‐plane tension. Effective control of fiber volume fraction and material composition necessitates a thorough comprehension of these phenomena as well as the capacity to predict them with accuracy. To solve this, a viscoelastic‐plastic model was put forth, which provides an account of the viscous effects on the fabric during its stages of compression and recovery. The proposed model incorporates changed Burgers units to manage time‐dependent deformations and plastic units to address permanent deformations. Through the application of a single set of parameters, the model precisely and comprehensively characterizes through‐thickness creep/recovery behavior of preformed dry fiber fabrics under varying conditions, including creep stress, temperature, and in‐plane tension. To enhance the practical utility of the model, an application has been developed and validated against experimental data conducted under diverse test conditions. The results demonstrate consistency between experimental curves and model‐predicted curves across various compression scenarios.Highlights A viscoelastic‐plastic model was proposed with a single parameter set. Stress, temperature, and in‐plane tension all exacerbated creep/recovery. Model captures temp. and time‐related creep/recovery with in‐plane tension. The model has been transformed into a practical application tool.

An Interpretable and Efficient Infinite-Order Vector Autoregressive Model for High-Dimensional Time Series

As a special infinite-order vector autoregressive (VAR) model, the vector autoregressive moving average (VARMA) model can capture much richer temporal patterns than the widely used finite-order VAR model. However, its practicality has long been hindered by its non-identifiability, computational intractability, and difficulty of interpretation, especially for high-dimensional time series. This article proposes a novel sparse infinite-order VAR model for high-dimensional time series, which avoids all above drawbacks while inheriting essential temporal patterns of the VARMA model. As another attractive feature, the temporal and cross-sectional structures of the VARMA-type dynamics captured by this model can be interpreted separately, since they are characterized by different sets of parameters. This separation naturally motivates the sparsity assumption on the parameters determining the cross-sectional dependence. As a result, greater statistical efficiency and interpretability can be achieved with little loss of temporal information. We introduce two l 1 -regularized estimation methods for the proposed model, which can be efficiently implemented via block coordinate descent algorithms, and derive the corresponding nonasymptotic error bounds. A consistent model order selection method based on the Bayesian information criteria is also developed. The merit of the proposed approach is supported by simulation studies and a real-world macroeconomic data analysis. Supplementary materials for this article are available online including a standardized description of the materials available for reproducing the work.

Short-term prediction of UT1-UTC and LOD via Dynamic Mode Decomposition and combination of least-squares and vector autoregressive model

Abstract This study presents a short-term forecast of UT1-UTC and LOD using two methods, i.e. Dynamic Mode Decomposition (DMD) and combination of Least-Squares and Vector Autoregression (LS+VAR). The prediction experiments were performed separately for yearly time spans, 2018-2022. The prediction procedure started on January 1 and ended on December 31, with 7-day shifts between subsequent 30-day forecasts. Atmospheric Angular Momentum data (AAM) were used as an auxiliary time series to potentially improve the prediction accuracy of UT1-UTC and LOD in LS+VAR procedure. An experiment was also conducted with and without elimination of effect of zonal tides from UT1-UTC and LOD time series. Two approaches to using the best steering parameters for the methods were applied:. First, an adaptive approach, which observes the rule that before every single forecast, a preliminary one must be performed on the pre-selected sets of parameters, and the one with the smallest prediction error is then used for the final prediction; and second, an averaged approach, whereby several forecasts are made with different sets of parameters (the same parameters as in adaptive approach) and the final values are calculated as the averages of these predictions. Depending on the method and data combination mean absolute prediction errors (MAPE) for UT1-UTC vary from 0.63 ms to 1.43ms for the 10th day and from 3.07 ms to 8.05ms for the 30th day of the forecast. Corresponding values for LOD vary from 0.110 ms to 0.245 ms for the 10th day and from 0.148 ms to 0.325 ms for the 30th day.

Calibration of Equivalent Viscous Damping Expressions for Displacement-Based Design and Application to RC Frames

Equivalent viscous damping plays a central role in displacement-based design procedures. In this paper, approaches for estimating the equivalent viscous damping of RC frame buildings are proposed. At first, the analytical formulation of Blandon and Priestley was analysed, and then a calibration of the coefficients of this formulation was performed. Compared with the work of Blandon and Priestley, a larger set of synthetic accelerograms, related to different types of soil and different intensities, and a wider range of the effective periods were considered. In particular, two different sets of parameters are proposed: the first is usable in the case of spectra obtained numerically (approach 1), and the second is usable in the case of code-based spectra and damping modification factor (approach 2). To test the performed calibration and to compare the considered formulations (i.e., the proposed and literature equations), the direct displacement-based design procedure has been applied to three case studies of reinforced concrete frame structures, and then pushover and nonlinear time-history analyses have been performed. The results show that the use of the calibrated parameters (for both the considered approaches) has determined more conservative results, in terms of design base shear and maximum drift from NLTH. Moreover, the average displacement profiles and the inter-storey drifts obtained from time-history analyses for the frames designed with the calibrated parameters match better the design profile.

Gold price prediction by a CNN-Bi-LSTM model along with automatic parameter tuning.

Banking and stock markets consider gold to be an important component of their economic and financial status. There are various factors that influence the gold price trend and its fluctuations. Accurate and reliable prediction of the gold price is an essential part of financial and portfolio management. Moreover, it could provide insights about potential buy and sell points in order to prevent financial damages and reduce the risk of investment. In this paper, different architectures of deep neural network (DNN) have been proposed based on long short-term memory (LSTM) and convolutional-based neural networks (CNN) as a hybrid model, along with automatic parameter tuning to increase the accuracy, coefficient of determination, of the forecasting results. An illustrative dataset from the closing gold prices for 44 years, from 1978 to 2021, is provided to demonstrate the effectiveness and feasibility of this method. The grid search technique finds the optimal set of DNNs' parameters. Furthermore, to assess the efficiency of DNN models, three statistical indices of RMSE, RMAE, and coefficient of determination (R2), were calculated for the test set. Results indicate that the proposed hybrid model (CNN-Bi-LSTM) outperforms other models in total bias, capturing extreme values and obtaining promising results. In this model, CNN is used to extract features of input dataset. Furthermore, Bi-LSTM uses CNN's outputs to predict the daily closing gold price.

Application of Machine Learning Methods for Process Optimization in Electronic Packaging Processes

Epoxy resins are commonly used as encapsulation materials in electronic packaging processes. Fluctuations in the materials lead to both changes in processability and to varying quality. Ideally, these variations should be identified, and measures taken as quickly as possible to reduce scrap parts and thus costs. A promising optimization approach for encapsulation processes are machine learning models, which have already shown good results in quality predictions, especially for injection molding. Subsequent quality measurements are avoided with good quality prediction models. With this type of models, not only predictions can be made, but also optimal parameter combinations can be found. In this paper, models for predicting quality criteria warpage and residual enthalpy of the epoxy molding compound were set up, trained and validated. Time series of in-situ sensors were used, from which relevant features were extracted and which, together with machine parameters, provide a dataset for prediction. The most promising prediction models are random forest regression and gradient boosting regression. T hey predict warpage with an accuracy of 90% to 91% and the residual enthalpy with an accuracy of 95%. Subsequently, optimization models of the machine parameters were set up. All relevant target variables were considered in a cost function, through the minimization of which an optimal parameter set was found. The gradient boosted tree and Bayesian optimization were determined to be the most promising models, as they lead to the lowest values of the respective cost function.

Geometrical and Numerical Analysis of Predator–Prey System Based on the Allee Effect in Predator

This study explores the complex dynamics of the predator–prey interactions, with a specific emphasis on the influence of the Allee effect on the predator population. We examined the fundamental mathematical characteristics of the model under consideration, such as the positivity of the system and the boundedness of the solutions. We investigated the equilibrium points and analyzed their stability using the Jacobi and Lyapunov methods. A comprehensive examination was carried out on the geometric properties of the dynamical system to compute the five invariants of the KCC theory. In particular, the deviation curvature tensor and its eigenvalues are investigated to demonstrate the behavior of the system stability. We have also obtained the necessary and sufficient conditions for the given set of parameters of the system in order to have the Jacobi stability (instability) near the equilibrium point. To visualize the dynamical behavior of the predator–prey model with the Allee effect in the predator density, numerical simulations were conducted. The investigation encompasses an examination of the system’s behavior from both geometric and numerical standpoints, with the objective of attaining a thorough comprehension using few examples.

The role of zooplankton in the growth of algal bloom: a mathematical study

Here a nonlinear mathematical model for an aquatic ecosystem containing both non-toxic and toxin-producing algal blooms is formulated and analyzed. The presence of harmful algae impacts the aquatic population, subsequently affecting the human population that relies on zooplankton (fish, crabs, etc.). It also deteriorates the water quality, and it is advisable not to use water from lakes containing harmful algae. Here, our focus is to understand the dynamics of aquatic ecosystems when we have both types of algae, one that is non-toxic and acts as food to zooplankton, and another that is toxin-producing algae that causes death to zooplankton. The predation of zooplankton on algae influences the growth of the algae population. First, we consider a deterministic model, and later, this model is extended to stochastic model to check whether it has any impact on the dynamics of the populations under consideration. Various equilibria of the proposed model are derived, and the local stability of these equilibria is thoroughly examined. The existence of Hopf-bifurcation is also demonstrated for a suitable set of parameters. The results of deterministic and stochastic models are compared using numerical simulation. Upon examining our results and simulation data, it is evident that modifying specific key parameters, such as the growth rate of non-toxic algae due to nutrient intake and the parameter associated with the predation of non-toxic algae by zooplankton, has a substantial impact on algal bloom dynamics. Minor adjustments to these parameters can result in an augmented presence of non-toxic algae and a simultaneous decrease in toxin-producing algae, aligning with the primary objectives set by policymakers.