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Journal articles on the topic 'Dulac'

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Published: 4 June 2021
Last updated: 4 February 2022

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1

Trifonov, S. I. "DIVERGENCE OF DULAC SERIES." Mathematics of the USSR-Sbornik 69, no. 1 (February 28, 1991): 37–56. http://dx.doi.org/10.1070/sm1991v069n01abeh001203.

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2

Osuna, Osvaldo, and Gabriel Villaseñor. "On the Dulac Functions." Qualitative Theory of Dynamical Systems 10, no. 1 (February 4, 2011): 43–49. http://dx.doi.org/10.1007/s12346-011-0036-y.

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3

Hryn, A. A., and S. V. Rudzevich. "Ways for detection of the exact number of limit cycles of autonomous systems on the cylinder." Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series 55, no. 2 (June 28, 2019): 182–94. http://dx.doi.org/10.29235/1561-2430-2019-55-2-182-194.

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For real autonomous systems of differential equations with continuously differentiable right-hand sides, the problem of detecting the exact number and localization of the second-kind limit cycles on the cylinder is considered. To solve this problem in the absence of equilibria of the system on the cylinder, we have developed our previously proposed ways consisting in a sequential two-step application of the Dulac – Cherkas test or the Dulac test. Additionally, a new way has been worked out using the generalization of the Dulac – Cherkas or Dulac test at the second step, where the requirement of constant sign for divergence is replaced by the transversality condition of the curves on which the divergence vanishes. With the help of the developed ways, closed transversal curves are found that divide the cylinder into subdomains surrounding it, in each of which the system has exactly one second-kind limit cycle.The practical efficiency of the mentioned ways is demonstrated by the example of a pendulum-type system, for which, in the absence of equilibria, the existence of exactly three second-kind limit cycles on the entire phase cylinder is proved.
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4

BROER, H. W., V. NAUDOT, and R. ROUSSARIE. "Catastrophe theory in Dulac unfoldings." Ergodic Theory and Dynamical Systems 26, no. 05 (July 26, 2006): 1363. http://dx.doi.org/10.1017/s0143385706000289.

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5

Stolovitch, Laurent. "Sur un théorème de Dulac." Annales de l’institut Fourier 44, no. 5 (1994): 1397–433. http://dx.doi.org/10.5802/aif.1439.

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6

Mourtada, Abderaouf, and Robert Moussu. "Applications de Dulac et applications pfaffiennes." Bulletin de la Société mathématique de France 125, no. 1 (1997): 1–13. http://dx.doi.org/10.24033/bsmf.2297.

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7

Dulac, Georges. "Notice : Larissa Albina par G. Dulac." Recherches sur Diderot et sur l'Encyclopédie 16, no. 1 (1994): 17–18. http://dx.doi.org/10.3406/rde.1994.1463.

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8

Chamberland, Marc, Anna Cima, Armengol Gasull, and Francesc Mañosas. "Characterizing asymptotic stability with Dulac functions." Discrete & Continuous Dynamical Systems - A 17, no. 1 (2007): 59–76. http://dx.doi.org/10.3934/dcds.2007.17.59.

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9

Osuna, O., J. Rodriguez, C. Vargas-De-Leon, and G. Villasenor. "Dulac functions for transformed vector fields." International Journal of Contemporary Mathematical Sciences 8 (2013): 291–97. http://dx.doi.org/10.12988/ijcms.2013.13031.

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10

CONNON, D. F. "Review. Editer Diderot. Dulac, Georges (ed.)." French Studies 44, no. 2 (April 1, 1990): 217. http://dx.doi.org/10.1093/fs/44.2.217-a.

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11

Giné, Jaume. "Dulac Functions of Planar Vector Fields." Qualitative Theory of Dynamical Systems 13, no. 1 (February 16, 2014): 121–28. http://dx.doi.org/10.1007/s12346-014-0108-x.

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12

Mardešić, P., and M. Resman. "Analytic moduli for parabolic Dulac germs." Russian Mathematical Surveys 76, no. 3 (June 1, 2021): 389–460. http://dx.doi.org/10.1070/rm10001.

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13

GAETA, GIUSEPPE. "RESONANT NORMAL FORMS AS CONSTRAINED LINEAR SYSTEMS." Modern Physics Letters A 17, no. 10 (March 28, 2002): 583–97. http://dx.doi.org/10.1142/s0217732302006825.

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We show that a nonlinear dynamical system in Poincaré–Dulac normal form (in ℝn) can be seen as a constrained linear system; the constraints are given by the resonance conditions satisfied by the spectrum of (the linear part of) the system and identify a naturally invariant manifold for the flow of the "parent" linear system. The parent system is finite dimensional if the spectrum satisfies only a finite number of resonance conditions, as implied e.g. by the Poincaré condition. In this case our result can be used to integrate resonant normal forms, and sheds light on the geometry behind the classical integration method of Horn, Lyapounov and Dulac.
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14

Carrasco Vidal, Nicole. "Función de Dulac en la Familia Loud." Proyecciones (Antofagasta) 36, no. 4 (December 2017): 769–78. http://dx.doi.org/10.4067/s0716-09172017000400769.

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15

Abate, Marco, and Jasmin Raissy. "Formal Poincaré-Dulac renormalization for holomorphic germs." Discrete & Continuous Dynamical Systems - A 33, no. 5 (2013): 1773–807. http://dx.doi.org/10.3934/dcds.2013.33.1773.

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16

Grin, A., K. R. Schneider, and L. Cherkas. "Dulac-Cherkas functions for generalized Liénard systems." Electronic Journal of Qualitative Theory of Differential Equations, no. 35 (2011): 1–23. http://dx.doi.org/10.14232/ejqtde.2011.1.35.

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17

Osuna, Osvaldo, and Gabriel Villaseñor-Aguilar. "Some properties of the Dulac functions set." Electronic Journal of Qualitative Theory of Differential Equations, no. 72 (2011): 1–8. http://dx.doi.org/10.14232/ejqtde.2011.1.72.

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18

Saez, E., and I. Szanto. "On the construction of certain Dulac functions." IEEE Transactions on Automatic Control 33, no. 9 (1988): 856. http://dx.doi.org/10.1109/9.1315.

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19

Yamanaka, Shogo. "Local Integrability of Poincaré–Dulac Normal Forms." Regular and Chaotic Dynamics 23, no. 7-8 (December 2018): 933–47. http://dx.doi.org/10.1134/s1560354718070080.

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20

Mardešić, P., M. Resman, J. P. Rolin, and V. Županović. "The Fatou coordinate for parabolic Dulac germs." Journal of Differential Equations 266, no. 6 (March 2019): 3479–513. http://dx.doi.org/10.1016/j.jde.2018.09.008.

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21

Osuna, Osvaldo, and Cruz Vargas-De-León. "Construction of Dulac functions for mathematical models in population biology." International Journal of Biomathematics 08, no. 03 (April 21, 2015): 1550035. http://dx.doi.org/10.1142/s1793524515500357.

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22

Hryn, A. A. "Dulac – Cherkas functions for systems equivalent to the van der Pol equation." Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series 56, no. 3 (October 18, 2020): 275–86. http://dx.doi.org/10.29235/1561-2430-2020-56-3-275-286.

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The object of this study is an autonomous van der Pol system on a real plane. The subject of the study is the properties of the limit cycle of this system. The main purpose of this paper is to find the localization of the limit cycle on the phase plane and establish its shape for various values of the real parameter of the van der Pol system. Our approach is based on the use of transverse curves related to the Dulac – Cherkas functions and approximating the location of the limit cycle. As the first step, five topologically equivalent systems, including systems with a parameter rotating the vector field, as well as singularly perturbed systems are determined for the van der Pol system. Then, applying the previously elaborated method, we constructed two polynomial Dulac – Cherkas functions for each of three systems from the considered ones in the phase plane for all real nonzero values of the parameter. Using them, transverse curves forming the boundaries of the localization regions of the limit cycle for the van der Pol system are found. Thus, the constructed Dulac – Cherkas functions allow us to determine the location of the limit cycle on the basis of algebraic curves for all real parameter values, including values close to the bifurcation of a limit cycle from the center ovals, the Andronov – Hopf bifurcation, and the bifurcation from a closed trajectory related to a discontinuous periodic solution.
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23

Mardešić, Pavao, David Marín, and Jordi Villadelprat. "Unfolding of resonant saddles and the Dulac time." Discrete & Continuous Dynamical Systems - A 21, no. 4 (2008): 1221–44. http://dx.doi.org/10.3934/dcds.2008.21.1221.

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24

Villaseñor-Aguilar, Gabriel, and Osvaldo Osuna. "On the Dulac functions for multiply connected domains." Electronic Journal of Qualitative Theory of Differential Equations, no. 61 (2013): 1–11. http://dx.doi.org/10.14232/ejqtde.2013.1.61.

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25

da Cruz, Leonardo P. C., and Joan Torregrosa. "A Bendixon–Dulac theorem for some piecewise systems." Nonlinearity 33, no. 5 (March 18, 2020): 2455–80. http://dx.doi.org/10.1088/1361-6544/ab6812.

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26

Andrew, Dudley. "Tami Williams, Germaine Dulac: A Cinema of Sensations." Nineteenth Century Theatre and Film 44, no. 1 (May 2017): 117–20. http://dx.doi.org/10.1177/1748372717714348.

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27

Cherkas, L. A., and A. A. Grin’. "On a Dulac function for the Kukles system." Differential Equations 46, no. 6 (June 2010): 818–26. http://dx.doi.org/10.1134/s0012266110060066.

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28

Zung, Nguyen Tien. "Convergence versus integrability in Poincaré-Dulac normal form." Mathematical Research Letters 9, no. 2 (2002): 217–28. http://dx.doi.org/10.4310/mrl.2002.v9.n2.a8.

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29

Gitschier, Jane. "Vive La Différence: An Interview with Catherine Dulac." PLoS Genetics 7, no. 6 (June 23, 2011): e1002140. http://dx.doi.org/10.1371/journal.pgen.1002140.

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30

Ciprian Foias, Luan Hoang, and Jean-Claude Saut. "NAVIER AND STOKES MEET POINCARÉAND DULAC." Journal of Applied Analysis & Computation 8, no. 3 (2018): 727–63. http://dx.doi.org/10.11948/2018.727.

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31

Mardešić, P., D. Marín, M. Saavedra, and J. Villadelprat. "Unfoldings of saddle-nodes and their Dulac time." Journal of Differential Equations 261, no. 11 (December 2016): 6411–36. http://dx.doi.org/10.1016/j.jde.2016.08.040.

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32

Amen, Azad Ibrahim. "On Limit Cycles of Planar Dynamical System Via Dulac- Cherkas Function." Journal of Zankoy Sulaimani - Part A 17, no. 2 (January 20, 2015): 45–50. http://dx.doi.org/10.17656/jzs.10379.

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33

MENDOZA, EMMANUEL, OSVALDO OSUNA, and GEISER VILLAVICENCIO-PULIDO. "FUNCIONES DE DULAC PARA MODELOS MATEMÁTICOS DE LA ECOLOGÍA." Revista de Matemática: Teoría y Aplicaciones 27, no. 2 (June 23, 2020): 387–402. http://dx.doi.org/10.15517/rmta.v27i2.34430.

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Excluir la existencia de oscilaciones sostenidas en modelos de la ecología matemática es de vital interés para conocer la dinámica poblacional de especies interactuando. En este trabajo se construyen funciones de Dulac para algunas generalizaciones de modelos usados comúnmente en la ecología matemática. Dicho resultado excluye la existencia de órbitas periódicas para algunos modelos que describen competencia intraespecífica o interespecífica, relaciones de competencia, de depredación y captura de individuos de alguna de las especies.
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34

Thomson, Ann. "Éditer Diderot, études recueillis par G. Dulac. SVEC, 1988." Recherches sur Diderot et sur l'Encyclopédie 7, no. 1 (1989): 154–55. http://dx.doi.org/10.3406/rde.1989.1038.

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35

Melnikov, Vitaly G. "Chebyshev economization in Poincaré–Dulac transformations of nonlinear systems." Nonlinear Analysis: Theory, Methods & Applications 63, no. 5-7 (November 2005): e1351-e1355. http://dx.doi.org/10.1016/j.na.2005.01.080.

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36

Flinn, Margaret C. "Germaine Dulac: A Cinema of Sensations by Tami Williams." French Forum 41, no. 3 (2016): 311–13. http://dx.doi.org/10.1353/frf.2016.0025.

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37

Polan, Dana. "Germaine Dulac: A Cinema of Sensations by Tami Williams." Film Quarterly 68, no. 3 (2015): 91–93. http://dx.doi.org/10.1525/fq.2015.68.3.91.

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38

Gaeta, Giuseppe, and Sebastian Walcher. "Dimension Increase and Splitting for Poincaré-Dulac Normal Forms." Journal of Nonlinear Mathematical Physics 12, sup1 (January 2005): 327–42. http://dx.doi.org/10.2991/jnmp.2005.12.s1.26.

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39

Mayne, Judith. "Germaine Dulac: A Cinema of Sensations. By Tami Williams." French Studies 70, no. 3 (May 13, 2016): 469–70. http://dx.doi.org/10.1093/fs/knw102.

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40

Moussu, R., and C. Roche. "Th�orie de Hovanskii et probl�me de Dulac." Inventiones Mathematicae 105, no. 1 (December 1991): 431–41. http://dx.doi.org/10.1007/bf01232274.

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41

Schilling, Derek. "Germaine Dulac: A Cinema of Sensations by Tami Williams." French Review 89, no. 1 (2015): 244–45. http://dx.doi.org/10.1353/tfr.2015.0181.

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42

Bonnot-Gallucci, Valécien. "L’Adaptation du Colomba de Prosper Mérimée par Germaine Dulac." 1895, no. 91 (June 1, 2020): 132–45. http://dx.doi.org/10.4000/1895.8023.

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43

Lafite, Clément. "La Reconstruction d’Âmes de Fous (1918) de Germaine Dulac." 1895, no. 91 (June 1, 2020): 82–95. http://dx.doi.org/10.4000/1895.8013.

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44

Grin, Alexander, and Klaus R. Schneider. "Study of the Bifurcation of a Multiple Limit Cycle of the Second Kind by Means of a Dulac–Cherkas Function: A Case Study." International Journal of Bifurcation and Chaos 26, no. 14 (December 30, 2016): 1650229. http://dx.doi.org/10.1142/s0218127416502291.

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We consider a generalized pendulum equation depending on the scalar parameter [Formula: see text] having for [Formula: see text] a limit cycle [Formula: see text] of the second kind and of multiplicity three. We study the bifurcation behavior of [Formula: see text] for [Formula: see text] by means of a Dulac–Cherkas function.
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45

Wuhaib, S. A., and N. F. Abd. "CONTROL OF PREY DISEASE IN STAGE STRUCTURE MODEL." Tikrit Journal of Pure Science 25, no. 2 (March 17, 2020): 129. http://dx.doi.org/10.25130/j.v25i2.968.

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In this paper, a mathematical model consisting of the prey-predator model, prey is at risk of disease then become as susceptible and infected, while predator with different stage structure: immature and mature predator, the infected prey is at risk recover and harvest. The function of disease is proportionality function. At the beginning, the reasons of studying stage structure and the dynamic of nontrivial subsystems that may be lead to coexistence of these types of spices explain and by using Maple software, Jacobean matrix, Routh-Hurwitz criterion, Bendixson-Dulac criterion and Lyapunov function to prove the existence, periodic solution, local and global stability. We concluded that the survival for two preys are possible through the non-periodic solution due to the Bendixson-Dulac criterion, also the immature predator neither attack preys nor yield offspring's and die when the mature predator extinction, the global stability conditions for the original system be stretch of global stability conditions for subsystems. Finally, Mathematica software employs to describe some results in numerical simulation http://dx.doi.org/10.25130/tjps.25.2020.040
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46

Liu, Xia, and Yepeng Xing. "Qualitative Analysis for a Predator Prey System with Holling Type III Functional Response and Prey Refuge." Discrete Dynamics in Nature and Society 2012 (2012): 1–11. http://dx.doi.org/10.1155/2012/678957.

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A predator prey system with Holling III functional response and constant prey refuge is considered. By using the Dulac criterion, we discuss the global stability of the positive equilibrium of the system. By transforming the system to a Liénard system, the conditions for the existence of exactly one limit cycle for the system are given. Some numerical simulations are presented.
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47

Cozzo, Laura Valeria. "Invitación a un viaje surrealista:." Saga. Revista de Letras, no. 8 (October 19, 2020): 258–66. http://dx.doi.org/10.35305/sa.vi8.28.

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Baudelaire ha inspirado a muchos artistas de diferentes disciplinas, el primer cine no iba a ser la excepción. Un ejemplo es la obra de Germaine Dulac, una directora y teórica francesa que ocupa un lugar remarcable en el panteón de artistas surrealistas, con su mediometraje L’invitation au voyage que ilustra de manera muy libre la poesía homónima incluida en Les fleurs du mal.
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48

Osuna, Osvaldo, Joel Rodríguez-Ceballos, Cruz Vargas-De-León, and Gabriel Villaseñor-Aguilar. "A note on the existence and construction of Dulac functions." Nonlinear Analysis: Modelling and Control 22, no. 4 (July 20, 2017): 431–40. http://dx.doi.org/10.15388/na.2017.4.1.

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49

Friel, Patrick. "Review: Germaine Dulac: A Cinema of Sensations, by Tami Williams." Afterimage 42, no. 3 (November 1, 2014): 38. http://dx.doi.org/10.1525/aft.2014.42.3.38.

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50

Li, Michael Y. "Dulac Criteria for Autonomous Systems Having an Invariant Affine Manifold." Journal of Mathematical Analysis and Applications 199, no. 2 (April 1996): 374–90. http://dx.doi.org/10.1006/jmaa.1996.0147.

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