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Bistability is a fundamental property of nonlinear systems and is found in many applied and theoretical studies of biological systems (populations and communities). In the simplest case it is expressed in the coexistence of diametrically opposed alternative stable equilibrium states of the system, and which of them will be achieved depends on the initial conditions. Bistability in simple models can lead to quad-stability as models become more complex, for example, when adding genetic, age and spatial structure. This occurs in different models from completely different subject area and leads to very interesting, often counterintuitive conclusions. In this article, we review such situations. The paper deals with bifurcations leading to bi- and quad-stability in mathematical models of the following biological objects. The first one is the system of two populations coupled by migration and under the action of natural selection, in which all genetic diversity is associated with a single diallelic locus with a significant difference in fitness for homo- and heterozygotes. The second is the system of two limited populations described by the Bazykin model or the Ricker model and coupled by migration. The third is a population with two age stages and density-dependent regulation of birth rate which is determined either only by population density, or additionally depends on the genetic structure of adjacent generations. We found that all these models have similar scenarios for the birth of equilibrium states that correspond to the formation of spatiotemporal inhomogeneity or to the differentiation by phenotypes of individuals from different age stages. Such inhomogeneity is a consequence of local bistability and appears as a result of a combination of pitchfork bifurcation (period doubling) and saddle-node bifurcation.

This paper investigates the effectiveness of Retrieval-Augmented Generation (RAG) combined with various Large Language Models (LLMs) for document retrieval and information access in corporate information systems. We survey typical use-cases of LLMs in enterprise environments, outline the RAG architecture, and discuss the major challenges that arise when integrating LLMs into a RAG pipeline. A system architecture is proposed that couples a text-vector encoder with an LLM. The encoder builds a vector database that indexes a library of corporate documents. For every user query, relevant contextual fragments are retrieved from this library via the FAISS engine and appended to the prompt given to the LLM. The LLM then generates an answer grounded in the supplied context. The overall structure and workflow of the proposed RAG solution are described in detail. To justify the choice of the generative component, we benchmark a set of widely used LLMs — ChatGPT, GigaChat, YandexGPT, Llama, Mistral, Qwen, and others — when employed as the answer-generation module. Using an expert-annotated test set of queries, we evaluate the accuracy, completeness, linguistic quality, and conciseness of the responses. Model-specific characteristics and average response latencies are analysed; the study highlights the significant influence of available GPU memory on the throughput of local LLM deployments. An overall ranking of the models is derived from an aggregated quality metric. The results confirm that the proposed RAG architecture provides efficient document retrieval and information delivery in corporate environments. Future research directions include richer context augmentation techniques and a transition toward agent-based LLM architectures. The paper concludes with practical recommendations on selecting an optimal RAG–LLM configuration to ensure fast and precise access to enterprise knowledge assets.

Seasonal migrations and herd instinct are traditionally recognized as wild reindeer (Rangifer tarandus L.) species-specific behavioral signs. These animals are forced to overcome water obstacles during the migrations. Behaviour peculiarities are considered as the result of the selection process, which has chosen among the sets of strategies, as the only evolutionarily stable one, determining the reproduction and biological survival of wild reindeer as a species. Natural processes in the Taimyr population wild reindeer are currently occurring against the background of an increase in the influence of negative factors due to the escalation of the industrial development of the Arctic. That is why the need to identify the ethological features of these animals completely arose. This paper presents the results of applying the classical methods of the theory of optimal control and differential games to the wild reindeer study of the migration patterns in overcoming water barriers, including major rivers. Based on these animals’ ethological features and behavior forms, the herd is presented as a controlled dynamic system, which presents also two classes of individuals: the leader and the rest of the herd, for which their models, describing the trajectories of their movement, are constructed. The models are based on hypotheses, which are the mathematical formalization of some animal behavior patterns. This approach made it possible to find the trajectory of the important one using the methods of the optimal control theory, and in constructing the trajectories of other individuals, apply the principle of control with a guide. Approbation of the obtained results, which can be used in the formation of a common “platform” for the adaptive behavior models systematic construction and as a reserve for the cognitive evolution models fundamental development, is numerically carried out using a model example with observational data on the Werchnyaya Taimyra River.

Technical carbon (soot) is a product obtained by thermal decomposition (pyrolysis) of hydrocarbons (usually oil) in a stream of heat carrier gas. Technical carbon is widely used as a reinforcing component in the production of rubber and plastic masses. Tire production uses 70% of all carbon produced. In furnace carbon production, the liquid hydrocarbon feedstock is injected into the natural gas combustion product stream through nozzles. The raw material is atomized and vaporized with further pyrolysis. It is important for the raw material to be completely evaporated before the pyrolysis process starts, otherwise coke, that contaminates the product, will be produced. It is impossible to operate without mathematical modeling of the process itself in order to improve the carbon production technology, in particular, to provide the complete evaporation of the raw material prior to the pyrolysis process. Mathematical modelling is the most important way to obtain the most complete and detailed information about the peculiarities of reactor operation.

A three-dimensional mathematical model and calculation method for raw material atomization and evaporation in the thermal gas flow are being developed in the FlowVision software package PC. Water is selected as a raw material to work out the modeling technique. The working substances in the reactor chamber are the combustion products of natural gas. The motion of raw material droplets and evaporation in the gas stream are modeled in the framework of the Eulerian approach of interaction between dispersed and continuous media. The simulation results of raw materials atomization and evaporation in a real reactor for technical carbon production are presented. Numerical method allows to determine an important atomization characteristic: average Sauter diameter. That parameter could be defined from distribution of droplets of raw material at each time of spray forming.

A critical analysis of existing approaches, methods and models to solve the problem of financial resources operational management has been carried out in the article. A number of significant shortcomings of the presented models were identified, limiting the scope of their effective usage. There are a static nature of the models, probabilistic nature of financial flows are not taken into account, daily amounts of receivables and payables that significantly affect the solvency and liquidity of the company are not identified. This necessitates the development of a new model that reflects the essential properties of the planning financial flows system — stochasticity, dynamism, non-stationarity.

The model for the financial flows distribution has been developed. It bases on the principles of optimal dynamic control and provides financial resources planning ensuring an adequate level of liquidity and solvency of a company and concern initial data uncertainty. The algorithm for designing the objective cash balance, based on principles of a companies’ financial stability ensuring under changing financial constraints, is proposed.

Characteristic of the proposed model is the presentation of the cash distribution process in the form of a discrete dynamic process, for which a plan for financial resources allocation is determined, ensuring the extremum of an optimality criterion. Designing of such plan is based on the coordination of payments (cash expenses) with the cash receipts. This approach allows to synthesize different plans that differ in combinations of financial outflows, and then to select the best one according to a given criterion. The minimum total costs associated with the payment of fines for non-timely financing of expenses were taken as the optimality criterion. Restrictions in the model are the requirement to ensure the minimum allowable cash balances for the subperiods of the planning period, as well as the obligation to make payments during the planning period, taking into account the maturity of these payments. The suggested model with a high degree of efficiency allows to solve the problem of financial resources distribution under uncertainty over time and receipts, coordination of funds inflows and outflows. The practical significance of the research is in developed model application, allowing to improve the financial planning quality, to increase the management efficiency and operational efficiency of a company.

Social media is a crucial indicator of the position of assets in the financial market. The paper describes the rigid solution for the classification problem to determine the influence of social media activity on financial market movements. Reputable crypto traders influencers are selected. Twitter posts packages are used as data. The methods of text, which are characterized by the numerous use of slang words and abbreviations, and preprocessing consist in lemmatization of Stanza and the use of regular expressions. A word is considered as an element of a vector of a data unit in the course of solving the problem of binary classification. The best markup parameters for processing Binance candles are searched for. Methods of feature selection, which is necessary for a precise description of text data and the subsequent process of establishing dependence, are represented by machine learning and statistical analysis. First, the feature selection is used based on the information criterion. This approach is implemented in a random forest model and is relevant for the task of feature selection for splitting nodes in a decision tree. The second one is based on the rigid compilation of a binary vector during a rough check of the presence or absence of a word in the package and counting the sum of the elements of this vector. Then a decision is made depending on the superiority of this sum over the threshold value that is predetermined previously by analyzing the frequency distribution of mentions of the word. The algorithm used to solve the problem was named benchmark and analyzed as a tool. Similar algorithms are often used in automated trading strategies. In the course of the study, observations of the influence of frequently occurring words, which are used as a basis of dimension 2 and 3 in vectorization, are described as well.

The problem of harvest optimization remains a central challenge in mathematical biology. The concept of Maximum Sustainable Yield (MSY), widely used in optimal exploitation theory, proposes maintaining target populations at levels ensuring maximum reproduction, theoretically balancing economic benefits with resource conservation. While MSYbased management promotes population stability and system resilience, it faces significant limitations due to complex intrapopulation structures and nonlinear dynamics in exploited species. Of particular concern are the evolutionary consequences of harvesting, as artificial selection may drive changes divergent from natural selection pressures. Empirical evidence confirms that selective harvesting alters behavioral traits, reduces offspring quality, and modifies population gene pools. In contrast, the genetic impacts of non-selective harvesting remain poorly understood and require further investigation.

This study examines how non-selective harvesting with constant removal rates affects evolution in genetically heterogeneous populations. We model genetic diversity controlled by a single diallelic locus, where different genotypes dominate at high/low densities: r-strategists (high fecundity) versus K-strategists (resource-limited resilience). The classical ecological and genetic model with discrete time is considered. The model assumes that the fitness of each genotype linearly depends on the population size. By including the harvesting withdrawal coefficient, the model allows for linking the problem of optimizing harvest with the that of predicting genotype selection.

Analytical results demonstrate that under MSY harvesting the equilibrium genetic composition remains unchanged while population size halves. The type of genetic equilibrium may shift, as optimal harvest rates differ between equilibria. Natural K-strategist dominance may reverse toward r-strategists, whose high reproduction compensates for harvest losses. Critical harvesting thresholds triggering strategy shifts were identified.

These findings explain why exploited populations show slow recovery after harvesting cessation: exploitation reinforces adaptations beneficial under removal pressure but maladaptive in natural conditions. For instance, captive arctic foxes select for high-productivity genotypes, whereas wild populations favor lower-fecundity/higher-survival phenotypes. This underscores the necessity of incorporating genetic dynamics into sustainable harvesting management strategies, as MSY policies may inadvertently alter evolutionary trajectories through density-dependent selection processes. Recovery periods must account for genetic adaptation timescales in management frameworks.

In general, solving the information explosion problem can be delegated to systems for automatic processing of digital data. These systems are intended for recognizing, sorting, meaningfully processing and presenting data in formats readable and interpretable by humans. The creation of intelligent knowledge extraction systems that handle unstructured data would be a natural solution in this area. At the same time, the evident progress in these tasks for structured data contrasts with the limited success of unstructured data processing, and, in particular, document processing. Currently, this research area is undergoing active development and investigation. The present paper is a systematic survey on both Russian and international publications that are dedicated to the leading trend in automatic text data processing: Text Mining (TM). We cover the main tasks and notions of TM, as well as its place in the current AI landscape. Furthermore, we analyze the complications that arise during the processing of texts written in natural language (NLP) which are weakly structured and often provide ambiguous linguistic information. We describe the stages of text data preparation, cleaning, and selecting features which, alongside the data obtained via morphological, syntactic, and semantic analysis, constitute the input for the TM process. This process can be represented as mapping a set of text documents to «knowledge». Using the case of stock trading, we demonstrate the formalization of the problem of making a trade decision based on a set of analytical recommendations. Examples of such mappings are methods of Information Retrieval (IR), text summarization, sentiment analysis, document classification and clustering, etc. The common point of all tasks and techniques of TM is the selection of word forms and their derivatives used to recognize content in NL symbol sequences. Considering IR as an example, we examine classic types of search, such as searching for word forms, phrases, patterns and concepts. Additionally, we consider the augmentation of patterns with syntactic and semantic information. Next, we provide a general description of all NLP instruments: morphological, syntactic, semantic and pragmatic analysis. Finally, we end the paper with a comparative analysis of modern TM tools which can be helpful for selecting a suitable TM platform based on the user’s needs and skills.

Social media posts play an important role in demonstration of financial market state, and their analysis is a powerful tool for trading. The article describes the result of a study of the impact of social media activities on the movement of the financial market. The top authoritative influencers are selected. Twitter posts are used as data. Such texts usually include slang and abbreviations, so methods for preparing primary text data, including Stanza, regular expressions are presented. Two approaches to the representation of a point in time in the format of text data are considered. The difference of the influence of a single tweet or a whole package consisting of tweets collected over a certain period of time is investigated. A statistical approach in the form of frequency analysis is also considered, metrics defined by the significance of a particular word when identifying the relationship between price changes and Twitter posts are introduced. Frequency analysis involves the study of the occurrence distributions of various words and bigrams in the text for positive, negative or general trends. To build the markup, changes in the market are processed into a binary vector using various parameters, thus setting the task of binary classification. The parameters for Binance candlesticks are sorted out for better description of the movement of the cryptocurrency market, their variability is also explored in this article. Sentiment is studied using Stanford Core NLP. The result of statistical analysis is relevant to feature selection for further binary or multiclass classification tasks. The presented methods of text analysis contribute to the increase of the accuracy of models designed to solve natural language processing problems by selecting words, improving the quality of vectorization. Such algorithms are often used in automated trading strategies to predict the price of an asset, the trend of its movement.

Simulation multiagent model of artificial life was created. Competitive ad-vantages of directed movement and diverse strategies of its using in population of protozoa in illumination gradient were considered. The results consistent with r-K selection theory were obtained. Agents behavior in artificial ecosystem are in qualitative agreement with behavior observed in nature.