Izvestiya Vysshikh Uchebnykh Zavedeniy-Prikladnaya Nelineynaya Dinamika最新文献

{"title":"Nonlinear elite generation change model","authors":"A. Kolesnikov, Georgij Malinetskii, Andrej Podlazov, S. Sirenko","doi":"10.18500/0869-6632-2022-30-4-456-479","DOIUrl":"https://doi.org/10.18500/0869-6632-2022-30-4-456-479","url":null,"abstract":"The purpose of the presented article was to build a concise conceptual mathematical model of the competitive dynamics of alternative types of social activity. The model was developed in the form of a discrete two-dimensional non-linear mapping. The proposed mapping is new and has not been previously studied either in the field of mathematical social dynamics (sociophysics), or in the section of discrete models of nonlinear dynamics. The approach we used corresponds to the ideas of the theory of social time put forward by F. Braudel. Nonlinear two-dimensional mapping, in a paradoxical way, given the general socio-economic ideas about the relationship between generations, as it turned out, has a Hamiltonian structure. The analysis showed that both formally and in terms of qualitative behavior it is close to the standard model describing a rotator under the action of impacts. It was found that, depending not only on the parameters of the problem, but also on the initial conditions, in this case, periodic, quasiperiodic, and chaotic dynamics are simultaneously possible. Within the framework of the model, this means a great variety of intergenerational relationships. Thus, the data in the system will not be “forgotten”. The influence on the dynamics of the model of “dissipative additions” describing the degradation of the elite, the desire of society to “eliminate the best” is demonstrated. The dynamics of the system and its dependence on parameters become much simpler; nevertheless, cyclicity and multistability do not disappear in it. In this approximation, history turns out to be “local” — the details and peculiarities of society’s behavior will be “forgotten” after several generations. The study of the constructed model opens up great prospects for the analysis of various types of cyclical processes in mathematical history.","PeriodicalId":41611,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedeniy-Prikladnaya Nelineynaya Dinamika","volume":"24 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77475020","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the conditions for safe connection to hub-cluster power grids","authors":"V. Khramenkov","doi":"10.18500/0869-6632-2022-30-4-424-435","DOIUrl":"https://doi.org/10.18500/0869-6632-2022-30-4-424-435","url":null,"abstract":"Purpose of this work is studying of the dynamics of a power grid model that results from the expansion of a highly centralized grid, i.e. a hub-cluster, by adding a small subgrid. The main attention is paid to the study of possible power grid operation regimes and their characteristics. Methods. Numerical simulation of power grid operation, the dynamics of which is described by the Kuramoto equations with inertia, is used. Results. Various power grid operation regimes and the boundaries of their existence in the parameter space are given. The main characteristics of these regimes, such as the probability of realization and the magnitude of oscillations of regime variables, are considered. The conditions for safe connection to hub-cluster power grids are obtained. Conclusion. The dynamics of power grid consisting of two subgrids and its operation regimes are considered. Based on the characteristics of these regimes, their safety for subgrids is determined. The results obtained made it possible to formulate conditions for a safe connection to hub-cluster power grids.","PeriodicalId":41611,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedeniy-Prikladnaya Nelineynaya Dinamika","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75917047","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Postulates of the cognitive theory of thinking and their consequences","authors":"V. Antonets","doi":"10.18500/0869-6632-2022-30-4-480-494","DOIUrl":"https://doi.org/10.18500/0869-6632-2022-30-4-480-494","url":null,"abstract":"Purpose of the work is to create a theoretical model of the thinking process, considered as a set of operations for the formation of cognitive generalizations of the level of categories (concepts). Method for creating a theoretical model is based on the approach used in natural sciences. It involves the selection of a small number of reliable facts, which are accepted as true on the basis of their evidence. On the basis of these facts, established in various scientific disciplines, the axioms of the proposed theory are formulated. Further, from the accepted axioms, they are logically deduced in the form of consequences: a) already known results that could be obtained in various fields of science, including those differing in the content of research, and therefore previously perceived as not related to each other; b) predictions of new connections and patterns in the study area. Results of the work are that it was possible to propose a version of the postulate dynamic theory of thinking, in which the main variables are the number of concepts formed, lost, realized and unconscious by the subject. The introduced postulates and variables made it possible to consider two types of models at the moment. Balanced integrodifferential models that describe the accumulation of the volume of conscious and unconscious concepts, as well as combinatorial models that describe the interactions of concepts. Conclusion. The proposed version of the dynamic thinking model made it possible to construct reasonable theoretical descriptions of the process of spontaneous language acquisition by bilingual children in a bilingual environment and a person’s ability to compare semantically heterogeneous objects with each other. The logical scheme of the approach and the concepts used in it made it possible to connect some facts known in psychology and in an explicitly compact formulation of the difference in the structure of scientific and artistic generalizations of the picture of the world.","PeriodicalId":41611,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedeniy-Prikladnaya Nelineynaya Dinamika","volume":"6 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88807442","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Variational approach to the construction of discrete mathematical model of the pendulum motion with vibrating suspension with friction","authors":"V. Savchin, P. Trinh","doi":"10.18500/0869-6632-2022-30-4-411-423","DOIUrl":"https://doi.org/10.18500/0869-6632-2022-30-4-411-423","url":null,"abstract":"The main purpose of this work is, first, a construction of the indirect Hamilton’s variational principle for the problem of motion of a pendulum with a vibration suspension with friction, oscillating along a straight line making a small angle with the vertical line. Second, the construction on its basis of the difference scheme. Third, to carry out its investigation by methods of numerical analysis. Methods. The problem of motion of the indicated pendulum is considering as a particular case of the given boundary problem for a nonlinear second order differential equations. For the solution of problem of its variational formulation there is used the criterion of potentiality of operators — the symmetry of the Gateaux derivative of nonlinear ˆ operator of the given problem. This criterion is also used for the construction of variational multiplier and the corresponding Hamilton’s variational principle. On its basis there is constructed and investigated a discrete analog of the given boundary problem and a problem of motion of the pendulum. Results. It is proved that the operator of the given boundary problem is not potential with respect to the classical bilinear form. There is found a variational multiplier and constructed the corresponding indirect Hamilton’s variational principle. On its basis there is obtained a discrete analog of the given boundary problem and its solution is found. As particular cases one can deduce from that the corresponding results for the problem of motion of the pendulum. There are performed numerical experiments, establishing the dependence of solutions of the problem of motion of the pendulum on the change of parameters. Conclusion. There is worked out a variational approach to the construction of two difference schemes for the problem of a pendulum with a suspension with friction, oscillating along a straight line making a small angle with the vertical line. There are presented results of numerical simulation under different parameters of the problem. Numerical results show that under sufficiently small amplitude and sufficiently big frequency of the oscillations of the point of suspension the pendulum realizes a periodical motion.","PeriodicalId":41611,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedeniy-Prikladnaya Nelineynaya Dinamika","volume":"24 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85956724","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Jacques Hadamard (1865–1963) — is the legend of mathematics and of absent-mindedness","authors":"D. Trubetskov","doi":"10.18500/0869-6632-2022-30-4-387-390","DOIUrl":"https://doi.org/10.18500/0869-6632-2022-30-4-387-390","url":null,"abstract":"This editorial is based on Hadamard's own statements and various recollections of him.","PeriodicalId":41611,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedeniy-Prikladnaya Nelineynaya Dinamika","volume":"2016 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75674566","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Reconstruction of integrated equations of periodically driven phase-locked loop system from scalar time series","authors":"M. Sysoeva, M. Kornilov, Lev Takaishvili, Valerij Matrosov, I. Sysoev","doi":"10.18500/0869-6632-2022-30-4-391-410","DOIUrl":"https://doi.org/10.18500/0869-6632-2022-30-4-391-410","url":null,"abstract":"Purpose of this work is to develop a reconstruction technique for the equations of a phase-locked loop system under periodic external driving from a scalar time series of one variable. Methods. Instead of the original model, we reconstructed a time-integrated model. So, since it is not necessary to evaluate the second derivative of the observable numerically, the method sensitivity to observation noise has significantly decreased. The external periodic driving is approximated with a trigonometric polynomial of time, the antiderivative of which is also a trigonometric polynomial. The assumption about continuity of an unknown nonlinear function is used to construct the target function for optimization. Results. It is shown that the proposed approach gives a significant advantage over the previously developed approach to the reconstruction of non-integrated equations, allowing to achieve acceptable parameter estimates with measurement noise being about 10% of the RMS deviation of the signal even in the presence of external driving. Conclusion. The described approach significantly extends the possibilities of reconstruction of phase-locked loop systems, allowing systems to be reconstructed under arbitrary periodic driving and at the same time significantly increasing noise resistance.","PeriodicalId":41611,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedeniy-Prikladnaya Nelineynaya Dinamika","volume":"2 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79077058","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Measuring cognitive potential based on the performance of tasks of various levels of complexity","authors":"A. Petukhov, S. Polevaia","doi":"10.18500/0869-6632-2022-30-3-311-321","DOIUrl":"https://doi.org/10.18500/0869-6632-2022-30-3-311-321","url":null,"abstract":"Purpose of work. The article is devoted to the topic of measuring the cognitive potential of a person on the basis of the obtained experimental data in order to identify its potential capabilities, as well as to monitor their dynamics, for example, to diagnose recovery after an illness. This goal is divided in the study into two tasks, namely, to assess the cognitive potential, it is necessary to develop two algorithms: 1. Assessment of the level of cognitive complexity of tasks. 2. Systems of levels of cognitive potential for an individual. Methods. The basis of the methods is a set of experimental, including specially developed author’s, techniques, as well as mathematical methods for processing data and calculating the entered specific parameters to formalize the cognitive potential. Results. On the basis of these methods, methods (and specific formulas) are proposed for calculating the cognitive potential of an individual using experimental data and tasks of various levels of complexity. Conclusion. Within the framework of this study, a methodology for determining the value of cognitive potential was created on the basis of the theory of information images / representations, as well as a specially developed web-toolkit for objectifying cognitive skills (including the so-called softskills). This value can be useful, both in studies related to changes in cognitive abilities as a result of the influence of various internal and external factors (for example, learning, diseases, injuries, etc.), diagnostic goals (for example, with the aim of determining the speed recovery after a disease that affects cognitive activity, such as a stroke or SARS-CoV-2), and in the formation of requirements for certain work positions that significantly depend on the cognitive abilities of the individual.","PeriodicalId":41611,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedeniy-Prikladnaya Nelineynaya Dinamika","volume":"28 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81767683","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Construction of the fitness function depending on a set of competing strategies based on the analysis of population dynamics","authors":"O. Kuzenkov","doi":"10.18500/0869-6632-2022-30-3-276-298","DOIUrl":"https://doi.org/10.18500/0869-6632-2022-30-3-276-298","url":null,"abstract":"The purpose of this work is to construct a fitness function that depends on the set of coexisting competing hereditary elements based on population dynamics in the “predator– prey” model with the logistic growth of prey. Materials and methods. The work uses the generalized Volterra model. The planktivorous fish plays the role of a predator. Many different species of zooplankton are considered as prey, which differ from each other in the hereditary strategies of daily vertical migrations. The model takes into account the intraspecific competition of prey. The peculiarity of the model consists of the presence of pairs of hereditary strategies in which the carriers of the first can displace the carriers of the second and vice versa — the carriers of the second can displace the carriers of the first, depending on the set of competing strategies in which they coexist. To restore the fitness function, the ranking method is used, which is reduced to the classification of ordered pairs of hereditary strategies into two classes “the first strategy displaces the second” and “the second displaces the first”. Results. The article presents a new methodology for constructing the fitness function. The technique involves two stages. First, the fitness function is reconstructed for a certain finite subset of elements on the basis of processing data on the long-term dynamics and comparing their competitive advantages. At the second stage, the form of the fitness function is derived for an arbitrary set of elements. It uses the features of interspecies interaction reflected in the model. With the help of the constructed fitness function, an evolutionarily stable regime of daily vertical migrations of zooplankton is modeled by numerically solving the minimax problem. Conclusion. The proposed method for constructing a fitness function that depends on a set of competing strategies is quite general and can be applied to a wide range of models of population dynamics. The strategy of diel vertical migrations of zooplankton constructed as a result of modeling is in good agreement with empirical data.","PeriodicalId":41611,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedeniy-Prikladnaya Nelineynaya Dinamika","volume":"58 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87571926","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"“Computer metaphor”, interhemispheral asymmetry and species (spontaneous) knowledge of Homo sapiens","authors":"N. Alexandrova","doi":"10.18500/0869-6632-2022-30-3-358-372","DOIUrl":"https://doi.org/10.18500/0869-6632-2022-30-3-358-372","url":null,"abstract":"The purpose of this article is to supplement the discussion in the field of research and modeling of the process of cognition first with data from neuropsychology and interhemispheric asymmetry, and second with reflections on species’ (spontaneous) knowledge of Homo sapiens. I. The data of neuropsychology and interhemispheric asymmetry signify two differently directed and complementary ways of processing information and regulating the functions inherent in the brain. One of these methods is analytical computer-like information processing, which is necessary for voluntary learning, the other method provides holistic-simultaneous, imaginative, unconscious, and involuntary processing. The duality of cognitive strategies is clearly manifested in the psychological analysis of syndromes in the case of brain lesions, as well as various conditions in healthy people (for example, in the case of bilingualism). II. Biological existence, which is the basis for all other layers of life, is provided by species-specific behavior and knowledge. Presumably species knowledge manifests itself as 1 — Constant involuntary assessment of the surrounding world and adequate reactions to changes in the world: from ordinary reactions (step aside, add a step, etc.) to the ability to react without hesitation in dangerous situations. 2 — The ability to understand connections between phenomena without scientific calculations. The entire history of mankind speaks of the existence of such an ability. People survived without science and created science along the way. 3 — Deep knowledge (often without the ability to logically explain) of what is natural and useful for us as representatives of the Homo Sapiens species, and of what is unnatural and harmful. There are reasons to assume that species knowledge is the basis that determines the common behavior of people of different eras and cultures in everything related to the continuation of the family and the cultivation of a new generation. Species knowledge merges together in the process of development with the knowledge gained during training.","PeriodicalId":41611,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedeniy-Prikladnaya Nelineynaya Dinamika","volume":"128 25 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79157155","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Neurodynamic model for creative cognition of relational networks with even cyclic inhibition","authors":"V. Tsukerman","doi":"10.18500/0869-6632-2022-30-3-331-357","DOIUrl":"https://doi.org/10.18500/0869-6632-2022-30-3-331-357","url":null,"abstract":"The purpose of this work is study of the neurodynamic foundations of the creative activity of the brain. Modern AI systems using deep neural network training require large amounts of input data, high computational costs and long training times. On the contrary, the brain can learn from small datasets in no time and, crucially, it is fundamentally creative. Methods. The study was carried out through computational experiments with neural networks containing 5 and 7 oscillatory layers (circuits) trained to represent abstract concepts of a certain class of animals. The scheme of neural networks with even cyclic inhibition (ECI networks) contains only bilateral inhibitory connections and consists of two subnets: a reference noncoding network, which is an analogue of the default brain mode neural network, and the main information network that receives time sequences of environmental signals and contextual inputs. After training, the reading of the population phase codes was performed with a simple linear decoder. Results. Conceptual learning of the network leads to the generation of a number of spatial abstract images that are distinguished by the most pronounced features of the relevant line of animals. In computational experiments, a wide set of isomorphic representations of concepts was obtained through: a) transformations of image spaces in a wide range of time scales of the training input signal flow, b) internal regulation of the time scales of mental representations of concepts, c) confirmation on the model of the dependence of psychological proximity of concepts on semantic distance; d) calling from memory (decoding) distributed groups of neurons of animal concepts, which the network has not been trained in. Conclusion. This paper shows for the first time how, using a small set of event input data (a sequence of 4 CCW and 2 CW signals) and very limited computational resources, ECI networks exhibit creative cognitions based on relational relationships, conceptual learning and generalization of knowledge.","PeriodicalId":41611,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedeniy-Prikladnaya Nelineynaya Dinamika","volume":"7 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82776296","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}