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Автор: Grafiati

Опубліковано: 10 грудня 2022

Оновлено: 28 січня 2023

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1

Bogoyavlenskij, O. I. "Integrable Lotka-Volterra systems." Regular and Chaotic Dynamics 13, no. 6 (December 2008): 543–56. http://dx.doi.org/10.1134/s1560354708060051.

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2

Christie, J. R., K. Gopalsamy, and Jibin Li. "Chaos in perturbed Lotka-Volterra systems." ANZIAM Journal 42, no. 3 (January 2001): 399–412. http://dx.doi.org/10.1017/s1446181100012025.

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Анотація:

AbstractLotka-Volterra systems have been used extensively in modelling population dynamics. In this paper, it is shown that chaotic behaviour in the sense of Smale can exist in timeperiodically perturbed systems of Lotka-Volterra equations. First, a slowly varying threedimensional perturbed Lotka-Volterra system is considered and the corresponding unperturbed system is shown to possess a heteroclinic cycle. By using Melnikov's method, sufficient conditions are obtained for the perturbed system to have a transverse heteroclinic cycle and hence to possess chaotic behaviour in the sense of Smale. Then a special case involving a reduction to a two-dimensional Lotka-Volterra system is examined, leading finally to an application with a model for the self-organisation of macromolecules.

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3

Mukhamedov, Farrukh, and Izzat Qaralleh. "Controlling Problem within a Class of Two-Level Positive Maps." Symmetry 14, no. 11 (October 31, 2022): 2280. http://dx.doi.org/10.3390/sym14112280.

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This paper aims to define the set of unital positive maps on M2(C) by means of quantum Lotka–Volterra operators which are quantum analogues of the classical Lotka–Volterra operators. Furthermore, a quantum control problem within the class of quantum Lotka–Volterra operators are studied. The proposed approach will lead to the understanding of the behavior of the classical Lotka–Volterra systems within a quantum framework.

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4

Redheffer, Ray. "Nonautonomous Lotka–Volterra Systems, I." Journal of Differential Equations 127, no. 2 (May 1996): 519–41. http://dx.doi.org/10.1006/jdeq.1996.0081.

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5

Redheffer, Ray. "Nonautonomous Lotka–Volterra Systems, II." Journal of Differential Equations 132, no. 1 (November 1996): 1–20. http://dx.doi.org/10.1006/jdeq.1996.0168.

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6

Feng, Chunhua, and Jianmin Huang. "Almost periodic solutions of nonautonomous Lotka–Volterra competitive systems with dominated delays." International Journal of Biomathematics 08, no. 02 (February 25, 2015): 1550019. http://dx.doi.org/10.1142/s1793524515500199.

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Анотація:

In this paper, a class of nonautonomous Lotka–Volterra type multispecies competitive systems with delays is studied. By employing Lyapunov functional, some sufficient conditions to guarantee the existence of almost periodic solutions for the Lotka–Volterra system are obtained.

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7

Fernandez, Juan C. Gutierrez, and Claudia I. Garcia. "On Lotka–Volterra algebras." Journal of Algebra and Its Applications 18, no. 10 (August 6, 2019): 1950187. http://dx.doi.org/10.1142/s0219498819501871.

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The purpose of this paper is to study the structure of Lotka–Volterra algebras, the set of their idempotent elements and their group of automorphisms. These algebras are defined through antisymmetric matrices and they emerge in connection with biological problems and Lotka–Volterra systems for the interactions of neighboring individuals.

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8

NAKATA, YUKIHIKO. "PERMANENCE FOR THE LOTKA–VOLTERRA COOPERATIVE SYSTEM WITH SEVERAL DELAYS." International Journal of Biomathematics 02, no. 03 (September 2009): 267–85. http://dx.doi.org/10.1142/s1793524509000716.

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In this paper, we establish a new sufficient condition of the permanence for the Lotka–Volterra cooperative systems with multiple discrete delays by extending the results in [Nakata and Muroya, Permanence for nonautonomous Lotka–Volterra cooperative systems with delays, Nonlinear Anal. RWA., in press]. Our condition holds even if the instantaneous feedback does not dominate over the total of the interspecific interactions and does not need the restriction on the size of time delays, different from the results in [Lu and Lu, Permanence for two-species Lotka–Volterra cooperative systems with delays, Math. Biosci. Eng.5 (2008) 477–484]. We offer an example for comparison with the previous results and numerical results supporting our theoretical analysis are given.

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9

Hou, Zhanyuan. "Permanence criteria for Kolmogorov systems with delays." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 144, no. 3 (May 16, 2014): 511–31. http://dx.doi.org/10.1017/s0308210512000297.

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In this paper, a class of Kolmogorov systems with delays are studied. Sufficient conditions are provided for a system to have a compact uniform attractor. Then Jansen's result for autonomous replicator and Lotka–Volterra systems has been extended to delayed non-autonomous Kolmogorov systems with periodic or autonomous Lotka–Volterra subsystems. Thus, simple algebraic conditions are obtained for partial permanence and permanence. An outstanding feature of all these results is that the conditions are independent of the size and distribution of the delays.

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10

Valero, José. "A Weak Comparison Principle for Reaction-Diffusion Systems." Journal of Function Spaces and Applications 2012 (2012): 1–30. http://dx.doi.org/10.1155/2012/679465.

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We prove a weak comparison principle for a reaction-diffusion system without uniqueness of solutions. We apply the abstract results to the Lotka-Volterra system with diffusion, a generalized logistic equation, and to a model of fractional-order chemical autocatalysis with decay. Moreover, in the case of the Lotka-Volterra system a weak maximum principle is given, and a suitable estimate in the space of essentially bounded functionsL∞is proved for at least one solution of the problem.

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11

Badri, Vahid. "Global observer for Lotka–Volterra systems." Systems & Control Letters 167 (September 2022): 105319. http://dx.doi.org/10.1016/j.sysconle.2022.105319.

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12

Kobayashi, Manami, Takashi Suzuki, and Yoshio Yamada. "Lotka-Volterra Systems with Periodic Orbits." Funkcialaj Ekvacioj 62, no. 1 (2019): 129–55. http://dx.doi.org/10.1619/fesi.62.129.

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13

Zeeman, M. L. "Extinction in competitive Lotka-Volterra systems." Proceedings of the American Mathematical Society 123, no. 1 (January 1, 1995): 87. http://dx.doi.org/10.1090/s0002-9939-1995-1264833-2.

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14

Yin, Juliang, Xuerong Mao, and Fuke Wu. "Generalized Stochastic Delay Lotka–Volterra Systems." Stochastic Models 25, no. 3 (July 22, 2009): 436–54. http://dx.doi.org/10.1080/15326340903088800.

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15

Grognard, F., and J. L. Gouzé. "POSITIVE CONTROL OF LOTKA-VOLTERRA SYSTEMS." IFAC Proceedings Volumes 38, no. 1 (2005): 417–22. http://dx.doi.org/10.3182/20050703-6-cz-1902.00724.

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16

Bogoyavlenskij, Oleg, Yoshiaki Itoh, and Tetsuyuki Yukawa. "Lotka–Volterra systems integrable in quadratures." Journal of Mathematical Physics 49, no. 5 (May 2008): 053501. http://dx.doi.org/10.1063/1.2912226.

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17

Ballesteros, Ángel, Alfonso Blasco, and Fabio Musso. "Integrable deformations of Lotka–Volterra systems." Physics Letters A 375, no. 38 (September 2011): 3370–74. http://dx.doi.org/10.1016/j.physleta.2011.07.055.

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18

Cressman, Ross, and József Garay. "Evolutionary stability in Lotka–Volterra systems." Journal of Theoretical Biology 222, no. 2 (May 2003): 233–45. http://dx.doi.org/10.1016/s0022-5193(03)00032-8.

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19

Mercado-Vásquez, Gabriel, and Denis Boyer. "Lotka–Volterra systems with stochastic resetting." Journal of Physics A: Mathematical and Theoretical 51, no. 40 (September 10, 2018): 405601. http://dx.doi.org/10.1088/1751-8121/aadbc0.

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20

Yi, Zhang. "Stability of Neutral Lotka–Volterra Systems." Journal of Mathematical Analysis and Applications 199, no. 2 (April 1996): 391–402. http://dx.doi.org/10.1006/jmaa.1996.0148.

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21

Liu, Meng, and Meng Fan. "Permanence of Stochastic Lotka–Volterra Systems." Journal of Nonlinear Science 27, no. 2 (October 12, 2016): 425–52. http://dx.doi.org/10.1007/s00332-016-9337-2.

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22

Teng, Zhidong. "Nonautonomous Lotka–Volterra Systems with Delays." Journal of Differential Equations 179, no. 2 (March 2002): 538–61. http://dx.doi.org/10.1006/jdeq.2001.4044.

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23

Muhammadhaji, Ahmadjan, Rouzimaimaiti Mahemuti, and Zhidong Teng. "Periodic Solutions for n-Species Lotka-Volterra Competitive Systems with Pure Delays." Chinese Journal of Mathematics 2015 (September 14, 2015): 1–11. http://dx.doi.org/10.1155/2015/856959.

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Анотація:

We study a class of periodic general n-species competitive Lotka-Volterra systems with pure delays. Based on the continuation theorem of the coincidence degree theory and Lyapunov functional, some new sufficient conditions on the existence and global attractivity of positive periodic solutions for the n-species competitive Lotka-Volterra systems are established. As an application, we also examine some special cases of the system, which have been studied extensively in the literature.

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24

Wang, Qi, Jingyue Yang, and Feng Yu. "Global well-posedness of advective Lotka–Volterra competition systems with nonlinear diffusion." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 150, no. 5 (April 3, 2019): 2322–48. http://dx.doi.org/10.1017/prm.2019.10.

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AbstractThis paper investigates the global well-posedness of a class of reaction–advection–diffusion models with nonlinear diffusion and Lotka–Volterra dynamics. We prove the existence and uniform boundedness of the global-in-time solutions to the fully parabolic systems under certain growth conditions on the diffusion and sensitivity functions. Global existence and uniform boundedness of the corresponding parabolic–elliptic system are also obtained. Our results suggest that attraction (positive taxis) inhibits blowups in Lotka–Volterra competition systems.

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25

Benhadri, Mimia, Tomás Caraballo, and Halim Zeghdoudi. "Existence of periodic positive solutions to nonlinear Lotka-Volterra competition systems." Opuscula Mathematica 40, no. 3 (2020): 341–60. http://dx.doi.org/10.7494/opmath.2020.40.3.341.

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Анотація:

We investigate the existence of positive periodic solutions of a nonlinear Lotka-Volterra competition system with deviating arguments. The main tool we use to obtain our result is the Krasnoselskii fixed point theorem. In particular, this paper improves important and interesting work [X.H. Tang, X. Zhou, On positive periodic solution of Lotka-Volterra competition systems with deviating arguments, Proc. Amer. Math. Soc. 134 (2006), 2967-2974]. Moreover, as an application, we also exhibit some special cases of the system, which have been studied extensively in the literature.

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26

Cantrell, Robert Stephen. "Global higher bifurcations in coupled systems of nonlinear eigenvalue problems." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 106, no. 1-2 (1987): 113–20. http://dx.doi.org/10.1017/s0308210500018242.

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SynopsisCoexistent steady-state solutions to a Lotka–Volterra model for two freely-dispersing competing species have been shown by several authors to arise as global secondary bifurcation phenomena. In this paper we establish conditions for the existence of global higher dimensional n-ary bifurcation in general systems of multiparameter nonlinear eigenvalue problems which preserve the coupling structure of diffusive steady-state Lotka–Volterra models. In establishing our result, we mainly employ the recently-developed multidimensional global multiparameter theory of Alexander–Antman. Conditions for ternary steady-state bifurcation in the three species diffusive competition model are given as an application of the result.

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27

Bountis, Tassos, Zhanat Zhunussova, Karlygash Dosmagulova, and George Kanellopoulos. "Integrable and non-integrable Lotka-Volterra systems." Physics Letters A 402 (June 2021): 127360. http://dx.doi.org/10.1016/j.physleta.2021.127360.

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28

SPAGNOLO, B., A. FIASCONARO, and D. VALENTI. "NOISE INDUCED PHENOMENA IN LOTKA-VOLTERRA SYSTEMS." Fluctuation and Noise Letters 03, no. 02 (June 2003): L177—L185. http://dx.doi.org/10.1142/s0219477503001245.

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Анотація:

We study the time evolution of two ecosystems in the presence of external noise and climatic periodical forcing by a generalized Lotka-Volterra (LV) model. In the first ecosystem, composed by two competing species, we find noise induced phenomena such as: (i) quasi deterministic oscillations, (ii) stochastic resonance, (iii) noise delayed extinction and (iv) spatial patterns. In the second ecosystem, composed by three interacting species (one predator and two preys), using a discrete model of the LV equations we find that the time evolution of the spatial patterns is strongly dependent on the initial conditions of the three species.

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29

Cairó, Laurent, and Jaume Llibre. "Darboux integrability for 3D Lotka-Volterra systems." Journal of Physics A: Mathematical and General 33, no. 12 (March 23, 2000): 2395–406. http://dx.doi.org/10.1088/0305-4470/33/12/307.

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30

Polcz, Péter. "Computational Stability Analysis of Lotka-Volterra Systems." Hungarian Journal of Industry and Chemistry 44, no. 2 (December 1, 2016): 113–20. http://dx.doi.org/10.1515/hjic-2016-0014.

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Анотація:

Abstract This paper concerns the computational stability analysis of locally stable Lotka-Volterra (LV) systems by searching for appropriate Lyapunov functions in a general quadratic form composed of higher order monomial terms. The Lyapunov conditions are ensured through the solution of linear matrix inequalities. The stability region is estimated by determining the level set of the Lyapunov function within a suitable convex domain. The paper includes interesting computational results and discussion on the stability regions of higher (3,4) dimensional LV models as well as on the monomial selection for constructing the Lyapunov functions. Finally, the stability region is estimated of an uncertain 2D LV system with an uncertain interior locally stable equilibrium point.

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31

Roeger, Lih-Ing Wu, and Glenn Lahodny. "Dynamically consistent discrete Lotka–Volterra competition systems." Journal of Difference Equations and Applications 19, no. 2 (November 4, 2011): 191–200. http://dx.doi.org/10.1080/10236198.2011.621894.

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32

Frachebourg, L., P. L. Krapivsky, and E. Ben-Naim. "Spatial organization in cyclic Lotka-Volterra systems." Physical Review E 54, no. 6 (December 1, 1996): 6186–200. http://dx.doi.org/10.1103/physreve.54.6186.

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33

Hernández-Bermejo, Benito, and Víctor Fairén. "Lotka-Volterra representation of general nonlinear systems." Mathematical Biosciences 140, no. 1 (February 1997): 1–32. http://dx.doi.org/10.1016/s0025-5564(96)00131-9.

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34

Redheffer, Ray. "Lotka–Volterra systems with constant interaction coefficients." Nonlinear Analysis: Theory, Methods & Applications 46, no. 8 (December 2001): 1151–64. http://dx.doi.org/10.1016/s0362-546x(00)00166-8.

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35

Dong, Lingzhen, and Yasuhiro Takeuchi. "Impulsive control of multiple Lotka–Volterra systems." Nonlinear Analysis: Real World Applications 14, no. 2 (April 2013): 1144–54. http://dx.doi.org/10.1016/j.nonrwa.2012.09.006.

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36

Delgado, M., and A. Suárez. "Age-dependent diffusive Lotka–Volterra type systems." Mathematical and Computer Modelling 45, no. 5-6 (March 2007): 668–80. http://dx.doi.org/10.1016/j.mcm.2006.07.013.

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37

Derrick, William, and Lee Metzgar. "Dynamics of Lotka-Volterra systems with exploitation." Journal of Theoretical Biology 153, no. 4 (December 1991): 455–68. http://dx.doi.org/10.1016/s0022-5193(05)80150-x.

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38

BOBIEŃSKI, MARCIN, and HENRYK ŻOŁĄDEK. "The three-dimensional generalized Lotka–Volterra systems." Ergodic Theory and Dynamical Systems 25, no. 3 (June 2005): 759–91. http://dx.doi.org/10.1017/s0143385704000902.

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39

Butler, G. J., and P. Waltman. "Persistence in three-dimensional lotka-volterra systems." Mathematical and Computer Modelling 10, no. 1 (1988): 13–16. http://dx.doi.org/10.1016/0895-7177(88)90117-3.

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40

de Oca, Francisco Montes, and Mary Lou Zeeman. "Extinction in nonautonomous competitive Lotka-Volterra systems." Proceedings of the American Mathematical Society 124, no. 12 (1996): 3677–87. http://dx.doi.org/10.1090/s0002-9939-96-03355-2.

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41

BAISHYA, M., and C. CHAKRABORTI. "Non-equilibrium fluctuation in volterra-lotka systems." Bulletin of Mathematical Biology 49, no. 1 (1987): 125–31. http://dx.doi.org/10.1016/s0092-8240(87)80037-x.

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42

López-Gómez, Julián, and Marcela Molina-Meyer. "Superlinear indefinite systems: Beyond Lotka–Volterra models." Journal of Differential Equations 221, no. 2 (February 2006): 343–411. http://dx.doi.org/10.1016/j.jde.2005.05.009.

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43

Liu, Meng, and Ke Wang. "Stochastic Lotka–Volterra systems with Lévy noise." Journal of Mathematical Analysis and Applications 410, no. 2 (February 2014): 750–63. http://dx.doi.org/10.1016/j.jmaa.2013.07.078.

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44

Hou, Zhanyuan. "Global attractor in competitive Lotka-Volterra systems." Mathematische Nachrichten 282, no. 7 (June 23, 2009): 995–1008. http://dx.doi.org/10.1002/mana.200610785.

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45

Baishya, M. C., and C. G. Chakraborti. "Non-equilibrium fluctuation in Volterra-Lotka systems." Bulletin of Mathematical Biology 49, no. 1 (January 1987): 125–31. http://dx.doi.org/10.1007/bf02459962.

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46

Kuang, Yang, and Hal L. Smith. "Convergence in Lotka–Volterra-type delay systems without instantaneous feedbacks." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 123, no. 1 (1993): 45–58. http://dx.doi.org/10.1017/s0308210500021235.

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Анотація:

SynopsisMost of the convergence results appearing so far for delayed Lotka–Volterra-type systems require that undelayed negative feedback dominate both delayed feedback and interspecific interactions. Such a requirement is rarely met in real systems. In this paper we present convergence criteria for systems without instantaneous feedback. Roughly, our results suggest that in a Lotka–Volterra-type system if some of the delays are small, and initial functions are small and smooth, then the convergence of its positive steady state follows that of the undelayed system or the corresponding system whose instantaneous negative feedback dominates. In particular, we establish explicit expressions for allowable delay lengths for such convergence to sustain.

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47

Korolkova, Anna, and Dmitry Kulyabov. "One-step Stochastization Methods for Open Systems." EPJ Web of Conferences 226 (2020): 02014. http://dx.doi.org/10.1051/epjconf/202022602014.

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48

Maier, Robert S. "The integration of three-dimensional Lotka–Volterra systems." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 469, no. 2158 (October 8, 2013): 20120693. http://dx.doi.org/10.1098/rspa.2012.0693.

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Анотація:

The general solutions of many three-dimensional Lotka–Volterra systems, previously known to be at least partially integrable, are constructed with the aid of special functions. Examples include certain ABC and May–Leonard systems. The special functions used are elliptic and incomplete beta functions. In some cases, the solution is parametric, with the independent and dependent variables expressed as functions of a ‘new time’ variable. This auxiliary variable satisfies a nonlinear third-order differential equation of a generalized Schwarzian type, and results of Carton-LeBrun on the equations of this type that have the Painlevé property are exploited, so as to produce solutions in closed form. For several especially difficult Lotka–Volterra systems, the solutions are expressed in terms of Painlevé transcendents. An appendix on incomplete beta functions and closed-form expressions for their inverses is included.

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49

Dukarić, Maša, and Jaume Giné. "Integrability of Lotka–Volterra Planar Complex Cubic Systems." International Journal of Bifurcation and Chaos 26, no. 01 (January 2016): 1650002. http://dx.doi.org/10.1142/s0218127416500024.

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In this paper, we study the Lotka–Volterra complex cubic systems. We obtain necessary conditions of integrability for these systems with some restriction on the parameters. The sufficiency is proved for all conditions, except one which remains open, using different methods.

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50

Han, Maoan, Jaume Llibre, and Yun Tian. "On the Zero-Hopf Bifurcation of the Lotka–Volterra Systems in R 3." Mathematics 8, no. 7 (July 12, 2020): 1137. http://dx.doi.org/10.3390/math8071137.

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Анотація:

Here we study 3-dimensional Lotka–Volterra systems. It is known that some of these differential systems can have at least four periodic orbits bifurcating from one of their equilibrium points. Here we prove that there are some of these differential systems exhibiting at least six periodic orbits bifurcating from one of their equilibrium points. We remark that these systems with such six periodic orbits are non-competitive Lotka–Volterra systems. The proof is done using the algorithm that we provide for computing the periodic solutions that bifurcate from a zero-Hopf equilibrium based in the averaging theory of third order. This algorithm can be applied to any differential system having a zero-Hopf equilibrium.

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