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Journal articles on the topic 'Bogdanov'

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Published: 4 June 2021

Last updated: 13 February 2022

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1

Morozova, Alla Yurievna. "«Physiological collectivism» of Alexander Bogdanov: idea and practice." Samara Journal of Science 9, no. 1 (February 28, 2020): 174–78. http://dx.doi.org/10.17816/snv202091208.

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The goal of the paper is to study the idea of physiological collectivism and attempts to implement it. This idea was proposed by Alexander Bogdanov (1873-1928), a philosopher, naturalist, and one of the leaders of Bolshevism, who saw it as the highest manifestation of collectivism, on the principles of which the society of the future would be based. In Bogdanovs opinion, a peculiar revolutionary meaning of blood transfusion consists in support of one organism by vital elements of another , in direct biophysical cooperation. In the last years of his life Bogdanov concentrated his efforts on the activity of the Institute of Blood Transfusion created by him and on the researches and experiments connected with blood transfusion, which he considered as practical realization of the idea of physiological collectivism. It is this story that is considered in the paper, but not from a medical point of view, but as one of the manifestations of Bogdanov-collectivist. The author of the paper considers various assumptions as to why in 1926 Bogdanov, who was disgraced and excommunicated from Bolshevism, was given the opportunity to create the Institute of Blood Transfusion, and comes to the conclusion that this decision was most likely dictated by the desire to channel Bogdanovs activity in the sphere as far from political life as possible. The paper also analyzes the circumstances of Bogdanovs death as a result of the experiment (the 12th exchange transfusion of blood) and concludes that it was not a suicide or a disguised murder, but a tragic accident associated with the lack of development of medical science at the time. This conclusion is based on the results of modern physicians research. The author of the paper emphasizes the role and importance of the activity of the Institute established by Bogdanov in the process of building the blood transfusion service in this country.

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2

Freebury-Jones, Darren. "Michael Bogdanov’s Iconoclastic Approach to Political Shakespeare." New Theatre Quarterly 35, no. 02 (April 15, 2019): 99–111. http://dx.doi.org/10.1017/s0266464x19000022.

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Between 1986 and 1989, Michael Bogdanov directed The Wars of the Roses (an ambitious seven-play Shakespeare cycle that won him the Olivier Award for Best Director in 1990), introducing an accessible and pertinent Shakespeare to 1980s audiences and paving the way for later politicized versions of Shakespeare’s plays – such as, recently, the New York Public Theater’s 2017 production of Julius Caesar. Following Bogdanov’s death in 2017, the time seems right for a new appraisal of his work as a radical, political director. The collection of Bogdanov’s personal papers at the Shakespeare Birthplace Trust offers a unique opportunity to gain an insight into the director’s mind. The papers include annotated scripts, production records, prompt books, reviews, programmes, unpublished manuscripts, and two volumes of The Director’s Cut – documents spanning Bogdanov’s entire theatrical career. In this article Darren Freebury-Jones engages with these materials, as well as the influences of theoretical movements such as cultural materialism on the director’s approach, in order to shed light on the ways in which Bogdanov stimulated and inspired new readings of Shakespeare’s history plays.

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3

Adams, Mark B. ""Red Star" Another Look at Aleksandr Bogdanov." Slavic Review 48, no. 1 (1989): 1–15. http://dx.doi.org/10.2307/2498682.

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In recent years, there has been a minor explosion of interest in Aleksandr Bogdanov and other radical Russian intellectuals of pre-Stalinist days. After being in limbo for half a century, their ideas seem almost fresh and vibrant: Set against subsequent Soviet history, their aborted visions of a socialist future seem to give a sense of what might have been. And who knows—in the Gorbachev period, as the Soviet Union sorts out its problems and policies, some of their ideas might enjoy a new lease on life. For these and other reasons, they have recently attracted special interest.Of course, in Bogdanov's case, there is much to be interested in. Born Aleksandr Aleksandrovich Malinovskii in 1873, Bogdanov trained as a physician in Moscow and Khar'kov, worked briefly as a psychiatrist, and published widely on philosophy, politics, social theory, social psychology, economics, and culture.

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4

Dontsova, O. A., T. S. Oretskaya, V. A. Sklyankina, and O. V. Shpanchenko. "Aleksei Alekseevich Bogdanov." Molecular Biology 39, no. 5 (September 2005): 625–30. http://dx.doi.org/10.1007/s11008-005-0078-9.

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5

Guckenheimer, John, and Yuri Kuznetsov. "Bogdanov-Takens bifurcation." Scholarpedia 2, no. 1 (2007): 1854. http://dx.doi.org/10.4249/scholarpedia.1854.

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6

Emelyanov, E. P. "PERIODIZATION OF WORLD HISTORY IN THE “SHORT COURSE OF ECONOMICS SCIENCE” BY ALEXANDER BOGDANOV." Вестник Пермского университета. История, no. 3(50) (2020): 56–66. http://dx.doi.org/10.17072/2219-3111-2020-3-56-66.

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The article is devoted to the problem of periodization of universal history in the work "A Short Course in Economic Science" written by Alexander Bogdanov. It analyzes the changes in the periodization of the historical process in various editions of the work, identifies the intellectual sources of those changes and establishes a connection between the evolution of Bogdanov’s historical concept and the development of historical science in the late 19th and early 20th centuries. The main direction in the evolution of Bogdanov’s historical views was the transition from a linear progressive scheme of world history to a description of history as a complex non-linear process in which periods of development are combined with periods of decline and stagnation. Abandoning the idea of steady linear progress, Bogdanov also abandoned the strict correspondence between a specific economic form and a certain historical era and concluded that various economic forms could coexist. The changes in Bogdanov’s approaches to the question of the role of economic forms in the periodization of world historical process testify to his search for special features specifying various eras in the history of mankind and reflect a general interest in the substantial characteristics of time characteristic of the European intellectual space of the first third of the 20th century

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7

Tracy, E. R., X. Z. Tang, and C. Kulp. "Takens-Bogdanov random walks." Physical Review E 57, no. 4 (April 1, 1998): 3749–56. http://dx.doi.org/10.1103/physreve.57.3749.

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8

Borukhov, V. T., and O. M. Kvetko. "Founded Lyapunov–Bogdanov Functionals." Differential Equations 56, no. 1 (January 2020): 29–38. http://dx.doi.org/10.1134/s0012266120010048.

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9

Ma, Li, Xianggang Liu, Xiaotong Liu, Ying Zhang, Yu Qiu, and Kaiyan Li. "On the Correlation Dimension of Discrete Fractional Chaotic Systems." International Journal of Bifurcation and Chaos 30, no. 12 (September 30, 2020): 2050174. http://dx.doi.org/10.1142/s0218127420501746.

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This paper is mainly devoted to the investigation of discrete-time fractional systems in three aspects. Firstly, the fractional Bogdanov map with memory effect in Riemann–Liouville sense is obtained. Then, via constructing suitable controllers, the fractional Bogdanov map is shown to undergo a transition from regular state to chaotic one. Meanwhile, the positive largest Lyapunov exponent is calculated by the Jacobian matrix algorithm to distinguish the chaotic areas. Finally, the Grassberger–Procaccia algorithm is employed to evaluate the correlation dimension of the controlled fractional Bogdanov system under different parameters. The main results show that the correlation dimension converges to a fixed value as the embedding dimension increases for the controlled fractional Bogdanov map in chaotic state, which also coincides with the conclusion driven by the largest Lyapunov exponent. Moreover, three-dimensional fractional Stefanski map is considered to further verify the effectiveness and generality of the obtained results.

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10

Merkuljev, A. V. "Propebela bogdanovi sp. nov. (Gastropoda, Conoidea, Mangeliidae) - a new species from Chukchi Sea and East Kamchatka." Ruthenica, Russian Malacological Journal 31, no. 1 (January 2, 2021): 1–6. http://dx.doi.org/10.35885/ruthenica.2021.31(1).1.

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In 1990 I.P. Bogdanov provided the new localities for Propebela fidicula - off the Wrangel Island in the Chukchi Sea and off the eastern coast of Kamchatka [Bogdanov, 1990]. These locations were far beyond the known range of this species - from Puget Sound Bay to the Aleutian Islands [Oldroyd, 1927]. Verification of material from the ZIN collection showed that the real Propebela fidicula in Russian waters is found only near the Commander Islands. The shells that Bogdanov identified as Propebela fidicula, belong to a new species. It differs from Propebela fidicula both in sculpture and radular morphology.

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11

ARROWSMITH, DAVID K., JULYAN H. E. CARTWRIGHT, ALEXIS N. LANSBURY, and COLIN M. PLACE. "THE BOGDANOV MAP: BIFURCATIONS, MODE LOCKING, AND CHAOS IN A DISSIPATIVE SYSTEM." International Journal of Bifurcation and Chaos 03, no. 04 (August 1993): 803–42. http://dx.doi.org/10.1142/s021812749300074x.

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We investigate the bifurcations and basins of attraction in the Bogdanov map, a planar quadratic map which is conjugate to the Hénon area-preserving map in its conservative limit. It undergoes a Hopf bifurcation as dissipation is added, and exhibits the panoply of mode locking, Arnold tongues, and chaos as an invariant circle grows out, finally to be destroyed in the homo-clinic tangency of the manifolds of a remote saddle point. The Bogdanov map is the Euler map of a two-dimensional system of ordinary differential equations first considered by Bogdanov and Arnold in their study of the versal unfolding of the double-zero-eigenvalue singularity, and equivalently of a vector field invariant under rotation of the plane by an angle 2π. It is a useful system in which to observe the effect of dissipative perturbations on Hamiltonian structure. In addition, we argue that the Bogdanov map provides a good approximation to the dynamics of the Poincare maps of periodically forced oscillators.

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12

Yassour, Avraham. "Letter on the Bogdanov Issue." Russian Review 49, no. 4 (October 1990): 467. http://dx.doi.org/10.2307/130527.

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13

Gare, Arran. "Aleksandr Bogdanov and Systems Theory." Democracy & Nature 6, no. 3 (November 2000): 341–59. http://dx.doi.org/10.1080/10855660020020230.

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14

Stiefenhofer, Matthias. "Unfolding Singularly Perturbed Bogdanov Points." SIAM Journal on Mathematical Analysis 32, no. 4 (January 2000): 820–53. http://dx.doi.org/10.1137/s0036141098334237.

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15

Jarvis, Andrew, and John Drakakis. "The “Marxism” of Michael Bogdanov." Shakespeare 14, no. 2 (April 3, 2018): 167–73. http://dx.doi.org/10.1080/17450918.2018.1455737.

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16

Häckl, G., and K. R. Schneider. "Controllability near Takens-Bogdanov points." Journal of Dynamical and Control Systems 2, no. 4 (October 1996): 583–98. http://dx.doi.org/10.1007/bf02254704.

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17

De Maesschalck, P., and F. Dumortier. "Slow–fast Bogdanov–Takens bifurcations." Journal of Differential Equations 250, no. 2 (January 2011): 1000–1025. http://dx.doi.org/10.1016/j.jde.2010.07.022.

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18

Teplyakov, Dmitriy A. "Anthropology Searches by Alexander Bogdanov." Vestnik Tomskogo gosudarstvennogo universiteta, no. 463 (February 1, 2021): 125–36. http://dx.doi.org/10.17223/15617793/463/16.

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19

Kurygin, A. A., I. S. Tarbaev, and V. V. Semenov. "Professor Fedor Rodionovich Bogdanov (1900–1973) (on the 120^th anniversary of the birthday)." Grekov's Bulletin of Surgery 179, no. 6 (April 2, 2021): 7–10. http://dx.doi.org/10.24884/0042-4625-2020-179-6-7-10.

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Professor Fedor Rodionovich Bogdanov was born on October 2 (15 in the Gregorian calendar), 1900. In 1919, Fedor successfully graduated from the classical men’s gymnasium and then entered the medical faculty of Rostov University. In 1930, F.R. Bogdanov and his wife moved to Sverdlovsk, where he became the head of the scientific and educational sector of the Institute and at the same time the head of the clinical department. There he actively studied the current and unresolved problem of treating intra-articular fractures at that time. In 1937, Fedor Rodionovich defended his doctoral thesis on the topic: «Reparative processes in intra-articular fractures and the principles of treatment of these fractures (experimental and clinical studies)». In 1958, F. R. Bogdanov moved to Kiev, where he was elected the head of the Department of Traumatology and Orthopedics of the Institute for Advanced Medical Studies and at the same time was appointed deputy director of the Kiev Research Institute of Traumatology and Orthopedics for scientific work. For all the time of his practical and scientific activity, F.R. Bogdanov was the academic advisor of 31 doctors and 86 candidates of medical sciences, the author and co-author of more than 200 scientific papers and 7 monographs. Professor Fedor Rodionovich Bogdanov died on March 27, 1973 and was buried at the Baikove Cemetery in Kiev.

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20

Makhnach, A. V., and A. I. Laktionova. "Family Resilience from the Perspective of A.A. Bogdanov’ Organizational Theory." Social Psychology and Society 12, no. 2 (2021): 41–55. http://dx.doi.org/10.17759/sps.2021120203.

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Objective. Analysis of the family resilience as its systemic characteristics from the standpoint of the organizational theory of A.A. Bogdanov. Background. The growing uncertainty of the existence of a person and a family makes such a quality as resilience in demand. The approach to the family as a system and practical work with it from the perspective of studying its resilience presupposes an emphasis not on the weakness and dysfunctionality of the family, but on those potential and real possibilities that are inherent in it. The family resilience as its systemic characteristic, depends on the balance of risk and protective factors, in the quality of which the family’s resources are considered. Family resourses are indicators of the family resilience. The resources of the nuclear family, contributing to the formation and maintenance of its resilience in wide temporal, social and cultural contexts, are gradually uniting individual resources. The process of forming the resource capacity of the family is not only their accumulation, but also the synthesis and grouping of the resources of the whole family as a system. Methodology. Organizational theory A.A. Bogdanov. Conclusions. Organizational theory A.A. Bogdanova, being a general scientific approach to the study of any system, makes it possible to analyze the family resilience as its systemic characteristics from the standpoint of the interaction of multidirectional activities mediated by differences in the understanding of family values, communication needs and organizational patterns. The joint coordinated activity of family members, leading to an increase in family resilience, is achieved with the help of certain resources.

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21

Antonov, Alexey. "On methodological individualism, holism and management in the light “Tectology” by A.A. Bogdanov." SHS Web of Conferences 116 (2021): 00064. http://dx.doi.org/10.1051/shsconf/202111600064.

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The consideration for the improvement of the efficiency of social economy made researchers look for names, views and methods which were not fully appreciated. This includes the general organizational science which occupies a prominent position by A.A. Bogdanov. There is no doubt that the ideas of A.A. Bogdanov are reflected in systems theory, cybernetics, medicine and philosophy of technology, aesthetics, linguistics and other disciplines. However they had little influence on economy, despite the fact that A.A. Bogdanov was a recognized expert in this area. This paper tries to fill this gap to some extent, and show that the ideas of Tectology are very relevant in modern economic discussions, including in the debate between methodological individualism and methodological holism. A.A. Bogdanov did not set out to study the organization of relations between people in the production process. This is the purpose of modern management. However, his approach to the study of the relationship between an individual and a team, the analysis of the conditions for the appearance of emergent effects in industrial cooperation deserve to be considered in economic theory and in management practice. Moreover, this is correlates to the modern trend to discover and study and, ultimately, use intangible factors of increasing the productivity of social economy in favor of man. In addition, the organizational views of the works of A.A. Bogdanov allow taking a fresh look at the real relationship between methodological holism and methodological individualism both in the structure of management and economy in general.

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22

ALGABA, A., M. MERINO, and A. J. RODRÍGUEZ-LUIS. "TAKENS–BOGDANOV BIFURCATIONS OF PERIODIC ORBITS AND ARNOLD'S TONGUES IN A THREE-DIMENSIONAL ELECTRONIC MODEL." International Journal of Bifurcation and Chaos 11, no. 02 (February 2001): 513–31. http://dx.doi.org/10.1142/s0218127401002286.

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In this paper we study Arnold's tongues in a ℤ2-symmetric electronic circuit. They appear in a rich bifurcation scenario organized by a degenerate codimension-three Hopf–pitchfork bifurcation. On the one hand, we describe the transition open-to-closed of the resonance zones, finding two different types of Takens–Bogdanov bifurcations (quadratic and cubic homoclinic-type) of periodic orbits. The existence of cascades of the cubic Takens–Bogdanov bifurcations is also pointed out. On the other hand, we study the dynamics inside the tongues showing different Poincaré sections. Several bifurcation diagrams show the presence of cusps of periodic orbits and homoclinic bifurcations. We show the relation that exists between two codimension-two bifurcations of equilibria, Takens–Bogdanov and Hopf–pitchfork, via homoclinic connections, period-doubling and quasiperiodic motions.

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23

Paranina, Alina, Lyudmila Chuikova, and Yuri Chuikov. "NIKOLAI BOGDANOV: PERSONALITY AND CULTURAL HERITAGE." Астраханский вестник экологического образования 19, no. 4 (2020): 174–86. http://dx.doi.org/10.36698/2304-5957-2020-19-4-174-186.

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24

Loktionov, Mikhail V. "Alexander Bogdanov: From Monism to Tectology." Russian Studies in Philosophy 57, no. 6 (November 2, 2019): 492–503. http://dx.doi.org/10.1080/10611967.2019.1670547.

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25

Bykova, Marina F. "Alexander Bogdanov and His Philosophical Legacy." Russian Studies in Philosophy 57, no. 6 (November 2, 2019): 477–81. http://dx.doi.org/10.1080/10611967.2019.1724043.

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26

Rowley, David G. "Bogdanov and Lenin: Epistemology and revolution." Studies in East European Thought 48, no. 1 (March 1996): 1–19. http://dx.doi.org/10.1007/bf02342514.

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27

Liu, Yanwei, Zengrong Liu, and Ruiqi Wang. "Bogdanov–Takens bifurcation with codimension three of a predator–prey system suffering the additive Allee effect." International Journal of Biomathematics 10, no. 03 (February 20, 2017): 1750044. http://dx.doi.org/10.1142/s1793524517500449.

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In the present work, research efforts have focused on investigating codimension two and three Bogdanov–Takens bifurcations of a predator–prey system with additive Allee effect. According to the existence conditions of Bogdanov–Takens bifurcation, we give the associated generic unfolding, and derive the dynamical classification in the perturbation parameter plane using some smooth parameter-dependent transformations of coordinate. Moreover, some numerical examples and simulations are performed to complete and illustrate our results.

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28

GUBERNOV, V. V., H. S. SIDHU, and G. N. MERCER. "DETECTING BOGDANOV–TAKENS BIFURCATION OF TRAVELING WAVES IN REACTION–DIFFUSION SYSTEMS." International Journal of Bifurcation and Chaos 16, no. 03 (March 2006): 749–55. http://dx.doi.org/10.1142/s0218127406015131.

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In this paper we investigate the onset of instabilities in a model describing the propagation of the steady planar premixed combustion wave. In particular, we are interested in determining the Bogdanov–Takens bifurcation condition, which is investigated semi-analytically. We derive an analytic condition for the existence of this type of bifurcation and based on this criterion we numerically determine the parameter values for which the Bogdanov–Takens bifurcation occurs. This numerical method is found to be more efficient than the previous methods.

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29

HUANG, JICAI, YIJUN GONG, and JING CHEN. "MULTIPLE BIFURCATIONS IN A PREDATOR–PREY SYSTEM OF HOLLING AND LESLIE TYPE WITH CONSTANT-YIELD PREY HARVESTING." International Journal of Bifurcation and Chaos 23, no. 10 (October 2013): 1350164. http://dx.doi.org/10.1142/s0218127413501642.

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The bifurcation analysis of a predator–prey system of Holling and Leslie type with constant-yield prey harvesting is carried out in this paper. It is shown that the model has a Bogdanov–Takens singularity (cusp case) of codimension at least 4 for some parameter values. Various kinds of bifurcations, such as saddle-node bifurcation, Hopf bifurcation, repelling and attracting Bogdanov–Takens bifurcations of codimensions 2 and 3, are also shown in the model as parameters vary. Hence, there are different parameter values for which the model has a limit cycle, a homoclinic loop, two limit cycles, or a limit cycle coexisting with a homoclinic loop. These results present far richer dynamics compared to the model with no harvesting. Numerical simulations, including the repelling and attracting Bogdanov–Takens bifurcation diagrams and corresponding phase portraits, and the existence of two limit cycles or an unstable limit cycle enclosing a stable multiple focus with multiplicity one, are also given to support the theoretical analysis.

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30

Kuznetsov, Yu A., H. G. E. Meijer, B. Al-Hdaibat, and W. Govaerts. "Accurate Approximation of Homoclinic Solutions in Gray–Scott Kinetic Model." International Journal of Bifurcation and Chaos 25, no. 09 (August 2015): 1550125. http://dx.doi.org/10.1142/s0218127415501254.

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The second-order predictor for the homoclinic orbit is applied to the Gray–Scott model. The problem is used to illustrate the approximation of the homoclinic orbits near a generic Bogdanov–Takens bifurcation in n-dimensional systems of differential equations. In the process, we show that it is necessary to take (usually ignored) cubic terms in the Bogdanov–Takens normal form into account to derive a correct second-order prediction for the homoclinic bifurcation curve. The analytic solutions are compared with those obtained by numerical continuation.

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31

van Ree, Erik. "Stalin's Bolshevism: The First Decade." International Review of Social History 39, no. 3 (December 1994): 361–81. http://dx.doi.org/10.1017/s0020859000112738.

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SummaryThis article discusses Stalin's Bolshevism during his Tiflis and Baku periods in the first decade of the century. It focuses on his position in the inner-faction debate between Lenin and Bogdanov. It holds that Dzhugashvili's tactical and organizational views in the years from 1907 to 1909 moved from sympathetic to Bogdanov to a position near Lenin, though remaining somewhat to the left of the latter. Dzhugashvili never belonged to the leftist tendency. He was a typical representative of the “Russian” praktiki, whose main concern was to further conciliation in the Bolshevik faction.

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32

Huang, Jicai, Xiaojing Xia, Xinan Zhang, and Shigui Ruan. "Bifurcation of Codimension 3 in a Predator–Prey System of Leslie Type with Simplified Holling Type IV Functional Response." International Journal of Bifurcation and Chaos 26, no. 02 (February 2016): 1650034. http://dx.doi.org/10.1142/s0218127416500346.

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It was shown in [Li & Xiao, 2007] that in a predator–prey model of Leslie type with simplified Holling type IV functional response some complex bifurcations can occur simultaneously for some values of parameters, such as codimension 1 subcritical Hopf bifurcation and codimension 2 Bogdanov–Takens bifurcation. In this paper, we show that for the same model there exists a unique degenerate positive equilibrium which is a degenerate Bogdanov–Takens singularity (focus case) of codimension 3 for other values of parameters. We prove that the model exhibits degenerate focus type Bogdanov–Takens bifurcation of codimension 3 around the unique degenerate positive equilibrium. Numerical simulations, including the coexistence of three hyperbolic positive equilibria, two limit cycles, bistability states (one stable equilibrium and one stable limit cycle, or two stable equilibria), tristability states (two stable equilibria and one stable limit cycle), a stable limit cycle enclosing a homoclinic loop, a homoclinic loop enclosing an unstable limit cycle, or a stable limit cycle enclosing three unstable hyperbolic positive equilibria for various parameter values, confirm the theoretical results.

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33

SPENCE, ALASTAIR, WU WEI, DIRK ROOSE, and BART DE DIER. "BIFURCATION ANALYSIS OF DOUBLE TAKENS–BOGDANOV POINTS OF NONLINEAR EQUATIONS WITH A Z2-SYMMETRY." International Journal of Bifurcation and Chaos 03, no. 05 (October 1993): 1141–53. http://dx.doi.org/10.1142/s0218127493000945.

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We consider the nonlinear equation f (x, Λ) = 0, f: X × ℝ3 → X, where X is a Banach space and f satisfies a Z2-symmetry relation. We are interested in a singular point (x0, Λ0) called a double Takens–Bogdanov point, where fx has a zero eigenvalue of geometric multiplicity 2 and algebraic multiplicity 3. We show that only three parameters are needed to recognise and compute this singular point when the Z2-symmetry is present. Paths of the following three kinds of singular points bifurcating at this double Takens–Bogdanov point are studied: double s-breaking fold points (where fx has a zero eigenvalue of algebraic and geometric multiplicity 2), Takens–Bogdanov points (a zero eigenvalue of geometric multiplicity 1 and algebraic multiplicity 2) and s-breaking G points (a simple zero eigenvalue and a pair of simple purely imaginary eigenvalues). The theory is developed in such a way as to produce nondegeneracy conditions and tests which may be utilised in numerical calculations. Numerical results are presented for the one-dimensional Brusselator model, described by a system of four reaction–diffusion equations.

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34

Rosenthal, Bernice Glatzer, and Zenovia A. Sochor. "Revolution and Culture: The Bogdanov-Lenin Controversy." American Historical Review 94, no. 5 (December 1989): 1441. http://dx.doi.org/10.2307/1906492.

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35

Tartarin, Robert. "Transfusion sanguine et immortalité chez Alexandr Bogdanov." Droit et société 28, no. 1 (1994): 565–81. http://dx.doi.org/10.3406/dreso.1994.1293.

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36

Kline, George L., and Zenovia Sochor. "Revolution and Culture: The Bogdanov-Lenin Controversy." Russian Review 50, no. 1 (January 1991): 96. http://dx.doi.org/10.2307/130226.

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37

Marot, John Eric. "The Bogdanov Issue: Reply to My Critics." Russian Review 49, no. 4 (October 1990): 457. http://dx.doi.org/10.2307/130526.

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38

Zeng, Bing, Shengfu Deng, and Pei Yu. "Bogdanov-Takens bifurcation in predator-prey systems." Discrete & Continuous Dynamical Systems - S 13, no. 11 (2020): 3253–69. http://dx.doi.org/10.3934/dcdss.2020130.

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39

Liu, Zhihua, and Rong Yuan. "Takens–Bogdanov singularity for age structured models." Discrete & Continuous Dynamical Systems - B 25, no. 6 (2020): 2041–56. http://dx.doi.org/10.3934/dcdsb.2019201.

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Tracy, E. R., and X. Z. Tang. "Anomalous scaling behavior in Takens-Bogdanov bifurcations." Physics Letters A 242, no. 4-5 (June 1998): 239–44. http://dx.doi.org/10.1016/s0375-9601(98)00200-x.

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41

Hirschberg, P., and E. Knobloch. "An unfolding of the Takens-Bogdanov singularity." Quarterly of Applied Mathematics 49, no. 2 (January 1, 1991): 281–87. http://dx.doi.org/10.1090/qam/1106393.

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Subashini, V. J., and S. Poornachandra. "Chaos Based Image Encryption Using Bogdanov Map." Journal of Computational and Theoretical Nanoscience 14, no. 9 (September 1, 2017): 4508–14. http://dx.doi.org/10.1166/jctn.2017.6768.

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Malonza, David Mumo. "Normal Forms for Coupled Takens-Bogdanov Systems." Journal of Nonlinear Mathematical Physics 11, no. 3 (January 2004): 376–98. http://dx.doi.org/10.2991/jnmp.2004.11.3.8.

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MALONZA, DAVID MUMO. "STANLEY DECOMPOSITION FOR COUPLED TAKENS–BOGDANOV SYSTEMS." Journal of Nonlinear Mathematical Physics 17, no. 1 (January 2010): 69–85. http://dx.doi.org/10.1142/s1402925110000647.

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Wang, Duo, Jing Li, Minhai Huang, and Young Jiang. "Unique Normal Form of Bogdanov–Takens Singularities." Journal of Differential Equations 163, no. 1 (April 2000): 223–38. http://dx.doi.org/10.1006/jdeq.1999.3739.

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Kuznetsov, Yu A., H. G. E. Meijer, B. Al Hdaibat, and W. Govaerts. "Improved Homoclinic Predictor for Bogdanov–Takens Bifurcation." International Journal of Bifurcation and Chaos 24, no. 04 (April 2014): 1450057. http://dx.doi.org/10.1142/s0218127414500576.

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Abstract:

An improved homoclinic predictor at a generic codim 2 Bogdanov–Takens (BT) bifucation is derived. We use the classical "blow-up" technique to reduce the canonical smooth normal form near a generic BT bifurcation to a perturbed Hamiltonian system. With a simple perturbation method, we derive explicit first- and second-order corrections of the unperturbed homoclinic orbit and parameter value. To obtain the normal form on the center manifold, we apply the standard parameter-dependent center manifold reduction combined with the normalization, that is based on the Fredholm solvability of the homological equation. By systematically solving all linear systems appearing from the homological equation, we remove an ambiguity in the parameter transformation existing in the literature. The actual implementation of the improved predictor in MatCont and numerical examples illustrating its efficiency are discussed.

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Coccolo, Mattia, BeiBei Zhu, Miguel A. F. Sanjuán, and Jesús M. Sanz-Serna. "Bogdanov–Takens resonance in time-delayed systems." Nonlinear Dynamics 91, no. 3 (December 19, 2017): 1939–47. http://dx.doi.org/10.1007/s11071-017-3992-1.

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Yassour, Avraham. "Philosophy ? Religion ? Politics: Borochov, Bogdanov and Lunacharsky." Studies in Soviet Thought 31, no. 3 (April 1986): 199–230. http://dx.doi.org/10.1007/bf01044978.

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Janovský, Vladimír, and Petr Plecháč. "Asymptotic analysis of perturbed Takens-Bogdanov points." Journal of Computational and Applied Mathematics 36, no. 3 (September 1991): 349–59. http://dx.doi.org/10.1016/0377-0427(91)90015-c.

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KUZNETSOV, YU A. "PRACTICAL COMPUTATION OF NORMAL FORMS ON CENTER MANIFOLDS AT DEGENERATE BOGDANOV–TAKENS BIFURCATIONS." International Journal of Bifurcation and Chaos 15, no. 11 (November 2005): 3535–46. http://dx.doi.org/10.1142/s0218127405014209.

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Abstract:

Simple computational formulas are derived for the two-, three-, and four-order coefficients of the smooth normal form on the center manifold at the Bogdanov–Takens (nonsemisimple double-zero) bifurcation for n-dimensional systems with arbitrary n ≥ 2. These formulas are equally suitable for both symbolic and numerical evaluation and allow one to classify all codim 3 Bogdanov–Takens bifurcations in generic multidimensional ODEs. They are also applicable to systems with symmetries. We perform no preliminary linear transformations but use only critical (generalized) eigenvectors of the linearization matrix and its transpose. The derivation combines the approximation of the center manifold with the normalization on it. Three known models are used as test examples to demonstrate advantages of the method.

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