Explicit Mathematical Model Research Articles

Leveraging MPPT capability for solar irradiance estimation: H-INC-IBS-based assessment of explicit models under real-world climatic conditions

This research investigates a low-cost method for estimating irradiance. The approach uses maximum power point tracking (MPPT) to easily estimate irradiance in a Photovoltaic (PV) system. Two main explicit mathematical models "IV-G" and "I-G" are examined for effective irradiance estimation. Given the requirement for MPPT, the examined PV system is powered by a hybrid-incremental conductance integral backstepping controller (H-INC-IBS), which enables proper maximum power point functioning. These models are evaluated using statistical indices such as the root mean square error (RMSE), mean absolute percentage error (MAPE), symmetrical mean absolute percentage error (SMAPE), and coefficient of correlation (R). The research tests these models using 37 climate patterns, demonstrating the influence of MPPT on model performance. In addition, the models are closely monitored in an experimental setup that includes two consecutive days of real-time climatic exposure. The experimental results show that the I-G model has the best accuracy measures, with worst MAE, MAPE, and SMAPE values of 18.81 W, 8.9039 %, and 4.7242 %, respectively. Thus, the article concludes that the I-G model is better suited for irradiance estimate in the context of MPPT. Furthermore, using evidence-based study outcomes, the paper proves that MPPT accuracy is proportional to estimating model accuracy. Given the little attention paid to this area of irradiance estimation, this work is intended to serve as a reference in the field.

Bridging the Gap Between Biological Plausibility and Practicality in Neuron Modeling: Challenges and Perspectives

Neuron modeling has been a fundamental approach in computational neuroscience for understanding the dynamics and function of the central nervous system (CNS). Over the past decades, a plethora of mathematical models, ranging from the seminal Hodgkin-Huxley model to more complex multicompartmental and stochastic models, have been developed to capture the intricate behavior of neurons and their interactions. However, despite the significant advances in modeling, there remains a substantial disconnect between the complexity of the models and their practical applicability in day-to-day medical and laboratory settings. This article explores the challenges and limitations of current neuron modeling approaches, particularly focusing on the trade-off between biological realism and computational tractability. I discuss the variability of neuronal properties within and across different regions of the brain, which poses a significant challenge for developing models that can accurately represent the full complexity of the CNS. I also highlight the computational bottlenecks associated with simulating highly detailed, which often require extensive computational resources and specialized software. Considering these challenges, we emphasize the need for a balance between biological plausibility and practicality in neuron modeling. We discuss the role of simplified models, such as the leaky integrate-and-fire (LIF) and Izhikevich models, which sacrifice some biological detail in favor of computational efficiency and ease of use. These models have proven valuable for large-scale simulations of neural networks and have provided important insights into the collective behavior of neuronal populations. Furthermore, I explore the potential of data-driven approaches, such as machine learning and artificial neural networks, in bridging the gap between biological realism and practical applicability. These approaches can learn the dynamics of neuronal systems directly from experimental data, bypassing the need for explicit mathematical models. I present a simple example using linear regression to predict neuronal firing rates based on input features, showcasing the potential of machine learning techniques in capturing the complex relationships between neuronal variables. I also highlight the need for more extensive validation of models against experimental data and the development of standardized benchmarks for assessing model performance. In conclusion, while the quest for biologically plausible neuron models has driven significant advances in our understanding of the CNS, the disconnect between model complexity and practical applicability remains a major challenge. By embracing simplified models, data-driven approaches, and interdisciplinary collaborations, we can work towards the development of more efficient and practical neuron models that can bridge the gap between biological realism and computational feasibility, ultimately facilitating the translation of theoretical insights into clinical and experimental applications.

Prediction of unconfined compressive strength of lime treated soils

ABSTRACT Robust models based on Artificial Neural Network and simplified linear regression were proposed to predict the Unconfined Compressive Strength (UCS) of Lime Treated Soils (LTS). In total, an experimental database using 1120 test specimens was created. Critical examination of the collected experimental data suggested that there are eight key parameters that govern the attained strength gain. These input parameters are liquid limit, plastic limit, dry unit weight, water content, fine content, lime content, curing temperature and curing time whereas the only output dependent parameter is the UCS. The parameters of the proposed model including weights, biases and transfer functions were successfully converted to an explicit mathematical model relating the UCS with the key input parameters. Based on the results of the statistical evaluation, it was shown that a three-layered Artificial-Neural-Network model with 19 hidden neurons was capable to predict the UCS of (LTS) with a high degree of accuracy that was better than that achieved by the developed regression model. A coupling effect of the input parameters and weights analysis were conducted for the developed Artificial-Neural-Network-model to assess the importance of the key parameters. Analysis of weights of the model showed that curing time was the most significant factor affecting strength gain.

Pressure from insect-resistant maize on protected butterflies and moths.

Intensification in agriculture affects many insect species, including butterflies. Insect-resistant crops, such as Bt (Bacillus thuringiensis) maize, which produces a toxin active against Lepidoptera, are an alternative to insecticide sprays. Genetically modified crops are regulated in most countries and require an environmental risk assessment. In the European Union, such assessments include the use of simulation models to predict the effects on nontarget Lepidoptera (NTL). To support the assessment of protected NTL, we extended an individual-based, stochastic, spatially explicit mathematical model (LepiX) to include a wider range of exposure scenarios, a species-sensitivity distribution, and an option for repeated exposure of individuals. We applied the model to transgenic maize DAS-1507, which expresses a high concentration of Bt toxin in pollen that may be consumed by NTL larvae on their host plants nearby. Even in the most conservative scenario without repeated exposure, mortality estimates for highly sensitive species ranged from 41% to 6% at distances of 10-1000 m from the nearest maize field. Repeated exposure can cause additional mortality and thus is relevant for the overall risk assessment. Uncertainties in both exposure and ecotoxicity estimates strongly influenced the predicted mortalities. Care should be taken to include these uncertainties in the model scenarios used for decision-making. In accordance with other modeling results, our simulations demonstrated that mean mortality may not be safe for protected species. With its high pollen expression, DAS-1507 maize may pose risks to sensitive and protected butterfly and moth species that may be difficult to manage. High expression of Bt toxin in pollen is unnecessary for controlling target pests. Consequently, we suggest that Bt maize with high pollen expression not be cultivated in regions where protected butterflies are to be conserved.

DEVELOPMENT AND CONFIGURATION OF A FULL-ORDER OBSERVER FOR «CABLE LINE – INDUCTION MOTOR» ELECTRICAL COMPLEX

Link for citation: Rakov I.V., Glazyrin A.S., Kladiev S.N. Development and configuration of a full-order observer for «cable line – induction motor» electrical complex. Bulletin of the Tomsk Polytechnic University. Geo Аssets Engineering, 2023, vol. 334, no. 10, рр. 219-231. In Rus. The relevance. The task of oil production specialists is to minimize all types of energy consumption, ensuring an increase in oil production profitability because of the following reasons. First of all, availability of oil reserves with low energy consumption decreases, and the number of gushing wells reduces, along with increase in water content in the extracted liquid. One of the methods of reducing energy consumption in wells with low and moderate flow rate, equipped with electric submersible pumps, is a well transfer from continuous to periodic operation mode, namely cyclic well operation. This involves alternating short periods of oil production (up to 15 minutes) with liquid accumulation (up to 30 minutes) in the wellbore. Well switching to a cyclic operation mode leads to a 40 % reduction in electric power consumption by the submersible electric motor, as well as increase in oil production up to 3 %. This can be achieved by partial gravitational separation of the extracted liquid at the accumulation stage. However, a negative consequence of switching to a cyclic operation mode is a reduction in an average time between failures. This is due to increase in current surges and torque during rapid acceleration of the submersible electric motor to the rated speed. Transition from a scalar control system with an open loop to a vector control system without sensors can settle these problems. To implement a vector control system, it is necessary to obtain information about the state variables of a submersible electric motor. Construction of a full-order observer based on explicit mathematical models is considered as a promising method of obtaining information, taking into account the main advantages and disadvantages of direct measurement and indirect estimation of state variables. Based on the above, the urgent task is to develop a full-cycle observer for the electromechanical complex «cable line – induction motor» and a methodology for its configuration. The settlement of this issue will create prerequisites for implementation of a vector control system by a submersible electric motor. The main aim: to develop and experimentally validate the effectiveness of a full-order observer for the electrical complex «cable line – induction motor» using voltage and current measurements at a cable line input. Methods: literature analysis, system analysis, mathematical modeling, experimental research. Results. The authors have developed and tested a full-order observer for the «cable line – induction motor» electrical complex. The results of this study confirm the efficiency of the developed observer and its potential applicability for implementing a vector control system for electric submersible pumps. Ultimately, this will enable the transition of low- and medium-flow-rate oil wells to a cyclically operated mode without a significant reduction of the mean time between failures.

Technical note: Seamless extraction and analysis of river networks in R

Abstract. Spatially explicit mathematical models are key to a mechanistic understanding of environmental processes in rivers. Such models necessitate extended information on networks' morphology, which is often retrieved from geographic information system (GIS) software, thus hindering the establishment of replicable script-based workflows. Here I present rivnet, an R package for GIS-free extraction and analysis of river networks based on digital elevation models (DEMs). The package exploits TauDEM's flow direction algorithm in user-provided or online accessible DEMs, and allows for computing covariate values and assigning hydraulic variables across any network node. The package is designed so as to require minimal user input while allowing for customization for experienced users. It is specifically intended for application in models of ecohydrological, ecological or biogeochemical processes in rivers. As such, rivnet aims to make river network analysis accessible to users unfamiliar with GIS-based and geomorphological methods and therefore enhance the use of spatially explicit models in rivers.

Model-Free HVAC Control in Buildings: A Review

The efficient control of HVAC devices in building structures is mandatory for achieving energy savings and comfort. To balance these objectives efficiently, it is essential to incorporate adequate advanced control strategies to adapt to varying environmental conditions and occupant preferences. Model-free control approaches for building HVAC systems have gained significant interest due to their flexibility and ability to adapt to complex, dynamic systems without relying on explicit mathematical models. The current review presents the recent advancements in HVAC control, with an emphasis on reinforcement learning, artificial neural networks, fuzzy logic control, and their hybrid integration with other model-free algorithms. The main focus of this study is a literature review of the most notable research from 2015 to 2023, highlighting the most highly cited applications and their contributions to the field. After analyzing the concept of each work according to its control strategy, a detailed evaluation across different thematic areas is conducted. To this end, the prevalence of methodologies, utilization of different HVAC equipment, and diverse testbed features, such as building zoning and utilization, are further discussed considering the entire body of work to identify different patterns and trends in the field of model-free HVAC control. Last but not least, based on a detailed evaluation of the research in the field, the current work provides future directions for model-free HVAC control considering different aspects and thematic areas.

An alternative approach to model the dynamics of a milling tool

Mathematical models play an increasing role in understanding and predicting machining processes, in particular milling. However, despite the considerable efforts that have been dedicated to this problem, a majority of milling models still rely on simplifying assumptions to calculate the chip thickness. In this paper, the chip thickness is determined without these simplifications, based on a surface function that describes the milled surface and on information about the workpiece boundary. By combining the partial differential equation (PDE) governing the evolution of this surface function with the ordinary differential equations (ODE) governing the tool/machine dynamics, a mixed PDE–ODE formulation is proposed to describe the dynamics of the milling process. The coupled system of differential equations is solved using an algorithm that combines finite difference (ODE) and finite volume (PDE) methods. A case study is presented to compare the proposed approach with the classical delay differential equations (DDE) model formulation for milling processes based on a simplified chip thickness model. The PDE–ODE formulation represents an explicit mathematical model for milling process dynamics; it yields a theoretically exact chip thickness and offers a means to assess the validity of models based on DDE formulation. Moreover, the proposed formulation is capable of simulating transient tool behaviors when the tool is milling the outer region of the workpiece, which is in general neglected by the DDE-based models.

A deep ensemble learning-driven method for the intelligent construction of structural hysteresis models

Accurate force–deformation hysteretic models for structures, components, and materials are essential for structural analysis. The development of an explicit mathematical model for hysteresis poses challenges in the fields of artificial model selection and precise and efficient calibration of key parameters. In recent years, deep learning-based implicit hysteresis model construction methods have been widely recognized. However, such methods exhibit instability and lack of generalization. By combining deep neural network feature extraction with physics-based explicit hysteresis models, it is possible to efficiently construct an accurate and stable force–deformation hysteresis model purely based on test data. Therefore, in this study, a sensitivity-guided long short-term memory neural networks (LSTM) method is proposed to extract the features of structural behaviors and predict the key parameters of explicit hysteresis models accurately and efficiently. Furthermore, an adaptive ensemble learning method based on multiple explicit hysteresis models is proposed to improve the generalization ability. Case studies on test results demonstrate that this method can accurately predict structural behaviors, which is more efficient than manual construction and has better generalization ability than classical data-driven hysteresis models.

Control of chaos with time-delayed feedback based on deep reinforcement learning

The time-delayed feedback control method, as one of popular methods for chaos control, is noninvasive and flexible for various dynamical systems from different fields of science and technology. In the method, however, an appropriate choice of the feedback gain is challenging, which requires the explicit mathematical model of the controlled system for stability analysis. Additionally, another limitation of the method is the so-called odd number limitation. The two problems restrict its application to practical situations. Fortunately, a technique called deep reinforcement learning is capable of learning the controlled environment (the dynamical system), by continually interacting with the controlled system, which makes it possible to obtain the right feedback gain without the requirement of the accurate mathematical model of the system. Hence, in this work, a time-delayed feedback control method based on deep reinforcement learning is put forward to solve the two problems. Compared with the traditional time-delayed feedback control, the proposed method, as a data-driven method due to the combination with deep reinforcement learning, offers a time-varying feedback gain according to the well-trained policy learned by the deep reinforcement learning algorithm. It maintains the non-invasive property of the time-delayed feedback control, but expands the operating range due to the time-varying feedback gain overcoming the odd number limitation. With numerical simulations, the proposed method is successfully applied to three different kinds of systems, the discrete logistic map, the non-autonomous Duffing oscillator and the autonomous Lorenz system.

Asymmetric Zipper-Coupled Tubes and Smooth Sheet Attachments in the Design of Deployable Space-Filling Mechanisms

AbstractZipper-coupled tubes are a unique structure consisting of two tubes with zig-zag walls that, when coupled in a zipper fashion, resist compression in the normal direction. A wider application of zipper-coupled tubes, however, is precluded by their angular form. By focusing on a subset of zipper-coupled tubes with parallel and coplanar creases constructed by repeating asymmetric degree-four vertex cells, we design a smooth sheet attachment that lies flat when the asymmetric zipper-coupled tubes are fully deployed, increasing the utility of the otherwise jagged tubes. Furthermore, we provide an explicit mathematical model of the motion of the resulting mechanism, thereby demonstrating its rigid-foldability.

Coordinated carbon capture systems and power-to-gas dynamic economic energy dispatch strategy for electricity–gas coupled systems considering system uncertainty: An improved soft actor–critic approach

Due to uncertainties in renewable energy generation and load demands, traditional energy dispatch schemes for an integrated electricity–gas system (IEGS) considerably depend on explicit forecast mathematical models. In this study, a novel data-driven deep reinforcement learning method is applied to solve the IEGS dynamic dispatch problem with the targets of minimizing carbon emission and operating cost. Moreover, a flexible operation of carbon capture system and power-to-gas facility is proposed to attain low operating costs. The IEGS dynamic dispatch problem is formulated as a Markov game, and a soft actor–critic (SAC) algorithm is applied to learn the optimal dispatch solution. To improve training efficiency and convergence, prioritized experience replay (PER) is employed. In the simulation, the proposed PER–SAC algorithm compared with deep Q-network and SAC has fast and stable learning performance. In contrast to a modified sequential quadratic programming based on uncertainty prediction, the proposed method can reduce the target cost by 11.62% when the prediction error exceeds 10%. The computational time of scenario analysis solution on the same hardware platform is 4.58 times than that of training the PER–SAC method. Finally, the simulation results under different scenarios demonstrate that the PER–SAC-based dispatch strategy has satisfactory generalization and adaptability.

МЕТОДИКА ОЦЕНИВАНИЯ ПАРАМЕТРОВ ЭЛЕКТРОТЕХНИЧЕСКОГО КОМПЛЕКСА «КАБЕЛЬНАЯ ЛИНИЯ — АСИНХРОННЫЙ ДВИГАТЕЛЬ» НА ОСНОВЕ БАЛАНСА ПОТРЕБЛЯЕМОЙ МОЩНОСТИ

Relevance In the Russian Federation, 82 % of oil is produced using Electric Submersible Pumps (ESP), while only 63 % of wells are equipped with such pumps. Since more than half of the operating wells are equipped with ESP, developing methods to reduce operating costs for these wells is a rational and logical allocation of human, material, and financial resources. One method to increase the profitability of oil production from low- and medium-flow rate wells is to transition a well equipped with ESP from continuous operation to intermittent operation, specifically cyclic operation. Intermittent operation reduces energy consumption by up to 40 % and increases oil production by 3 % due to partial gravitational separation of the produced fluid during accumulation. However, the negative effect of transitioning to intermittent operation is reflected in the reduction of the average runtime before failure due to a decreased ESP hydroprotection resource, accelerated wear of the pump unit thrust bearings, and intermediate radial bearings. The cause of these negative effects is the increased vibration level during intensive startup. One way to address these issues is transitioning from the existing scalar open-loop control system to a vector sensorless control system for the ESP. To implement such a system, it is necessary to obtain information about the vector of the ESP state variables. A promising approach to obtaining information about the ESP state involves creating observers based on explicit mathematical models. To create an observer for the state variables, mathematical models for each component of the studied system must be developed and combined into a unified system. When measuring currents and voltages at the output of the step-up transformer, the studied system will be an electric complex «Cable Line — Induction Motor». To implement this observer, it is necessary to determine the parameters of the equivalent circuit of the studied complex. Based on the above, developing a methodology for identifying the parameters of the equivalent circuit of the electric complex «Cable Line — Induction Motor» when measuring currents and voltages on the surface is a timely and relevant task. Solving this task will create prerequisites for the implementation of a vector control system for the ESP, increasing the reliability of the ESP during intermittent operation, and consequently, increasing the profitability of oil production from low- and medium-flow rate oil wells. Aim of research To develop and experimentally confirm the effectiveness of a methodology for assessing the parameters of the electric complex «Cable Line — Induction Motor» based on the balance of consumed power. Research methods Analysis of literary sources, system analysis, mathematical modeling, experimental research. Results The effectiveness of the methodology for assessing the parameters of the electric complex «Cable Line — Induction Motor» based on the balance of consumed power has been experimentally tested and confirmed.

Estimating the effect of the wMel release programme on the incidence of dengue and chikungunya in Rio de Janeiro, Brazil: a spatiotemporal modelling study

Introgression of genetic material from species of the insect bacteria Wolbachia into populations of Aedes aegypti mosquitoes has been shown in randomised and non-randomised trials to reduce the incidence of dengue; however, evidence for the real-world effectiveness of large-scale deployments of Wolbachia-infected mosquitoes for arboviral disease control in endemic settings is still scarce. A large Wolbachia (wMel strain) release programme was implemented in 2017 in Rio de Janeiro, Brazil. We aimed to assess the effect of this programme on the incidence of dengue and chikungunya in the city. 67 million wMel-infected mosquitoes were released across 28 489 locations over an area of 86·8 km² in Rio de Janeiro between Aug 29, 2017 and Dec 27, 2019. Following releases, mosquitoes were trapped and the presence of wMel was recorded. In this spatiotemporal modelling study, we assessed the effect of the release programme on the incidence of dengue and chikungunya. We used spatiotemporally explicit mathematical models applied to geocoded dengue cases (N=283 270) from 2010 to 2019 and chikungunya cases (N=57 705) from 2016 to 2019. On average, 32% of mosquitoes collected from the release zones between 1 month and 29 months after the initial release tested positive for wMel. Reduced wMel introgression occurred in locations and seasonal periods in which cases of dengue and chikungunya were historically high, with a decrease to 25% of mosquitoes testing positive for wMel during months in which disease incidence was at its highest. Despite incomplete introgression, we found that the releases were associated with a 38% (95% CI 32-44) reduction in the incidence of dengue and a 10% (4-16) reduction in the incidence of chikungunya. Stable establishment of wMel in the geographically diverse, urban setting of Rio de Janeiro seems to be more complicated than has been observed elsewhere. However, even intermediate levels of wMel seem to reduce the incidence of disease caused by two arboviruses. These findings will help to guide future release programmes. Bill & Melinda Gates Foundation and the European Research Council.

Externalities modulate the effectiveness of the Wolbachia release programme

Externalities modulate the effectiveness of the Wolbachia release programme

Phase plane analysis applied to non-explicit multibody vehicle models

A new methodology for constructing stability maps (phase-plane analysis) is presented and validated for application to complex multibody vehicle models implemented in Multibody Dynamics simulation software (Adams®). Traditional methodologies are developed to be applied to explicit mathematical models. Given the complexity of some special multibody systems, particularly in vehicle dynamics, simplifications are needed to apply this stability analysis technique. The main limitation when using simplified models is the need to neglect components which could have a significant influence on the dynamic behavior of the system and therefore on its stability. In the proposed methodology it is not necessary to have access to explicit mathematical models of multibody systems. Thus, the stability map of a vehicle model can be constructed by considering highly nonlinear dynamic elements, such as tires and silent-blocks components, modeled using the nonlinear finite element technique.

Artificial neural networks for prediction of COVID-19 in India by using backpropagation.

The COVID‐19 pandemic has affected thousands of people around the world. In this study, we used artificial neural network (ANN) models to forecast the COVID‐19 outbreak for policymakers based on 1st January to 31st October 2021 of positive cases in India. In the confirmed cases of COVID‐19 in India, it's critical to use an estimating model with a high degree of accuracy to get a clear understanding of the situation. Two explicit mathematical prediction models were used in this work to anticipate the COVID‐19 epidemic in India. A Boltzmann Function‐based model and Beesham's prediction model are among these methods and also estimated using the advanced ANN‐BP models. The COVID‐19 information was partitioned into two sections: training and testing. The former was utilized for training the ANN‐BP models, and the latter was used to test them. The information examination uncovers critical day‐by‐day affirmed case changes, yet additionally unmistakable scopes of absolute affirmed cases revealed across the time span considered. The ANN‐BP model that takes into consideration the preceding 14‐days outperforms the others based on the archived results. In forecasting the COVID‐19 pandemic, this comparison provides the maximum incubation period, in India. Mean square error, and mean absolute percent error have been treated as the forecast model performs more accurately and gets good results. In view of the findings, the ANN‐BP model that considers the past 14‐days for the forecast is proposed to predict everyday affirmed cases, especially in India that have encountered the main pinnacle of the COVID‐19 outbreak. This work has not just demonstrated the relevance of the ANN‐BP techniques for the expectation of the COVID‐19 outbreak yet additionally showed that considering the incubation time of COVID‐19 in forecast models might produce more accurate assessments.

Mathematical study on gravity effect of the liquid bridge between two rigid spheres

To better understand how gravity affects the evolution of capillary force and meniscus shape of the vertical liquid bridge between two millimeter-size spheres, an explicit mathematical model was built using Surface Evolver software. In this study, the rupture behavior of liquid bridge in the equilibrium state was studied using the energy minimization method, and the validity of the mathematical method followed was verified by comparing with existing research results. In addition, the gravity effect on the meniscus shape and geometric parameters were systematically studied. Finally, the gravity effect on the residual liquid volume after the liquid bridge ruptures was examined, and a calculation method for the residual liquid volume on the sphere was proposed, which was proven by mathematical methods and experiments. The relative error was <16% when the liquid dripping error was neglected, proving the feasibility of the calculation method.

The Adaptive Significance of Flash Behavior: A Bayesian Model

Some cryptic animals have conspicuous color patches that are displayed when they move. This “flash behavior” may serve several functions, but perhaps the most widely invoked explanation is that the display makes it harder for the signaler to be found by predators once it has settled. There is now some experimental evidence that flash behavior while fleeing can enhance the survivorship of prey in the manner proposed. However, to date there has been no explicit mathematical model to help understand the way in which flash displays might interfere with the search process of predators. Here we apply Bayesian search theory to show that the higher the conspicuousness of a prey item, the sooner a predator should give up searching for it in an area where it appears to have settled, although the relationship is not always monotonically decreasing. Thus, fleeing prey that give the impression of being conspicuous will tend to survive at a higher rate than prey seen to flee in their cryptic state, since predators search for flashing prey for an inappropriately short period of time. The model is readily parameterized and makes several intuitive predictions including: (1) the more confident a predator is that a prey item has settled in a given area, the longer it will search there, (2) the more conspicuous the flash display, the greater its effect in reducing predation, (3) flash behavior will especially benefit those prey with an intermediate level of crypsis when at rest, and (4) the success of flash displays depends on the predator being uncertain of the prey’s resting appearance. We evaluate the empirical evidence for these predictions and discuss how the model might be further developed, including the incorporation of mimicry which would maintain the deception indefinitely.

Spatially explicit multi-objective mathematical model for invasive species management

Spatially explicit multi-objective mathematical model for invasive species management