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Miklós Farkas’ scientific publications
Books
Special Functions with Applications to Engineering and Physics, Műszaki Könyvkiadó, Budapest, 1964, pp. 416 (in Hungarian).
(with I. Farkas), Introduction to Linear Algebra, Adam Hilger Ltd. & Akadémiai Kiadó, London & Budapest, 1975, pp. 205.
Periodic Motions, Springer, Berlin, 1994, pp. 577.
Dynamical Models in Biology, Academic Press, New York, 2001, pp. 200.
Papers
Discussion of the geometry of affinely connected spaces by direct method, Publ. Math. Debrecen, 8 (1961), 25–54.
On differential geometric investigation of ordinary differential equations, International Congress of Mathematicians, 1962, Stockholm, 74.
Differential-geometric investigation of a certain class of second-order ordinary differential equations, Mat. Lapok, 13 (1962), 289–297 (in Hungarian).
Constructing affinely connected spaces by direct method, Trudy Sem. Vector Tensor Anal. (Moscow State Univ.), 12 (1963), 5–6 (in Russian).
A proof of Gauss-Bonnet’s theorem, Nigerian J. Sci., 1 (1967), 175–178.
On stability of geodesics, Abacus (J. Math. Assoc. Nigeria), 6 (1967), 25–28.
On stability and geodesics, Ann. Univ. Sci. Budapest, Sect. Math., 11 (1968), 145–159.
Controllably periodic perturbations of autonomous systems, Congres International des Mathématiciens, Nice, 1970, 228.
Controllably periodic perturbations of autonomous systems, Acta Math. Acad. Sci. Hungar., 22 (1971), 337–348.
Determination of controllably periodic perturbed solutions by Poincaré’s method, Studia Sci. Math. Hungar., 7 (1972), 257–266.
(with R. A. Karim), On controllably periodic perturbations of Liénard’s equation, Per. Polytechnica Budapest, Sect. Electr. Eng., 16 (1972), 4–45.
(with I. Farkas), On perturbations of van der Pol’s equation, Ann. Univ. Sci. Budapest, Sect. Math., 15 (1972), 155–164.
On the conditional extremum, Mat. Lapok, 24 (1973/75), 113–129 (in Hungarian).
On isolated periodic solutions of differential systems, Ann. Mat. Pura Appl. (4), 106 (1975), 233–243.
A dynamic theory of simultaneous learning, Alk. Mat. Lapok, 2 (1976/77), 103–114 (in Hungarian).
On a qualitative characterization of processes, Alk. Mat. Lapok, 2 (1976/77), 237–257 (in Hungarian).
Estimates on the existence regions of perturbed periodic solutions, SIAM J. Math. Anal., 9 (1978), 876–890.
A model of the development of the societal system in catastrophe theory, Magyar Filoz. Szemle, 22 (1978), 802–808 (in Hungarian).
(with A. Lőkös and I. Mile), The effect of simultaneous learning on the accession of knowledge, Magyar Pedagógia, 18 (1978), 220–225 (in Hungarian).
Isolation of trajectories of periodic solutions of systems of differential equations, Trudy Moskov. Orden. Lenin. Energet. Inst., 357 (1978), 107–108 (in Russian).
A model of the development of the societal system in catastrophe theory, Acta Philos. Acad. Sci. Hungar., 5 (1978), 235–244.
(with J. Fritz and P. Michelberger), On the effect of stochastic road profiles on vehicles travelling with varying speed, Acta Techn. Acad. Sci. Hungar., 91 (1980), 303–319.
The attractor of Duffing’s equation under bounded perturbation, Ann. Mat. Pura Appl. (4), 128 (1980), 123–132.
(with A. Lőkös and I. Mile), A dynamic model of simultaneous memorization, Acta Cient. Venezolana, 32 (1981), 132–137.
Attractors of systems close to periodic ones, Nonlin. Anal., 5 (1981), 845–851.
Attractors of systems close to autonomous ones, Acta Sci. Math. (Szeged), 44 (1982), 329–334.
Mathematics and objective reality, Acta Cient. Venezolana, 33 (1982), 275–279.
Attractors of systems under bounded perturbation, Proc. Equadiff No. 5 (Bratislava, 1981), Teubner, Leipzig, 1982, 91–94.
The attractor of perturbed van der Pol’s equation, Z. Angew. Math. Mech., 63 (1983), T44–T45.
Duffing’s equation under bounded perturbation, Proc. Int. Conf. Nonlin. Oscillations No. 9 (Kiev, 1981), Vol. I, Naukova Dumka, Kiev, 1984, 371–373.
Stable oscillations in a predator prey model with time lag, J. Math. Anal. Appl., 102 (1984), 175–188.
Stability of bifurcating orbits in a predator-prey model, Mathematical Modelling in Science and Technology (Zürich, 1983), Pergamon Press, Oxford, 1984, 925–927.
Zip bifurcation in a competition model, Nonlin. Anal., 8(1984), 1295–1309.
A cusp model for the evolution of the social systems, Science of Science, 4 (1984), 285–293.
Stable coexistence and bifurcations in population dynamics, Alk. Mat. Lapok, 10 (1984), 203–229 (in Hungarian).
A zip bifurcation arising in population dynamics, Proc. Int. Conf. Nonlin. Oscillations No. 10 (Varna, 1984), Bulgarian Acad. Sci., Sofia, 1985, 150–155.
(with A. Farkas and L. Kajtár), On Hopf bifurcation in a predator-prey model, Differential Equations: Qualitative Theory (Szeged, 1984), Vol. I, North Holland, Amsterdam, 1986, 283–290.
(with L. Sparing and G. Szabó), On Hopf bifurcation of Rayleigh’s equation, Per. Polytechnica Budapest, Sect. Mech. Eng., 30 (1986), 263–271.
Competitive exclusion by zip bifurcation, Dynamical Systems (Sopron 1985), Lecture Notes in Economics and Mathematical Systems 287, Springer, Berlin, 1987, 165–178.
(with B. M. Garay, G. Szabo, L. Szépkúti and I. V. Nagy), Modeling of depth filtration, Ann. Univ. Sci. Budapest, Sect. Comput., 7 (1987), 67–73.
(with Z. Gaspár, L. Kollár, G. Patkó, L. Pomázi and G. Stépán), Stability investigations of mechanical systems: state of art, Acta Techn. Acad. Sci. Hungar., 100 (1987), 67–99.
(with A. Bródy), Forms of economic motion, Közgazd. Szemle, 34 (1987), 1178–1184 (in Hungarian).
(with A. Farkas and G. Szabó), Bifurcation charts for predator-prey models with memory, Proc. Int. Conf. Nonlin. Oscillations No. 11 (Budapest, 1987), J. Bolyai Math. Soc., Budapest, 1987, 808–811.
(with A. Bródy), Forms of economic motion, Acta Oecon. Acad. Sci. Hungar., 38 (1987), 361–370.
(with A. Farkas), Stable oscillations in a more realistic predator-prey model with time lag, Asymptotic Methods of Mathematical Physics (Kiev, 1987), Naukova Dumka, Kiev, 1988, 250–256.
(with A. Farkas and G. Szabó), Multiparameter bifurcation diagrams in predator-prey models with time lag, J. Math. Biol., 26 (1988), 93–103.
(with H. I. Freedman), The stable coexistence of competing species on a renewable resource, J. Math. Anal. Appl., 138 (1989), 461–472.
(with H. I. Freedman), Stability conditions for two predator one prey systems, Evolution and Control in Biological Systems (Luxenburg, 1987), Acta Appl. Math., 14 (1989), 3–10.
On the stability of one-predator two-preys systems, G. J. Butler Mem. Conf. Diff. Equat. Math. Biol. (Edmonton, 1988), Rocky Mountain J. Math., 20 (1990), 909–916.
On the local stability of n predators (preys) one prey (predator) systems, Qualitative Theory of Diff. Equat. (Szeged, 1988), North Holland, Amsterdam, 1990, 181–191.
(with A. Dancsó, H. Farkas and G. Szabó), Hopf bifurcation in some chemical models, React. Kinet. Catal. Lett., 42 (1990), 325–330.
(with S. Gyökér), On robustness of stable food chains, Acta Cient. Venezolana, 42 (1991), 9–12.
(with A. Dancso, H. Farkas and G. Szabó), Investigations into a class of generalized two-dimensional Lotka-Volterra schemes, Acta Appl. Math., 23 (1991), 103–127.
(with G. Stépán), On perturbations of the kernel in infinite delay systems, Z. Angew. Math. Mech., 72 (1992), 153–156.
(with M. Kotsis), Modelling predator-prey and wage-employment dynamics, Dynamic Economic Models and Optimal Control (Vienna, 1991), North-Holland, Amsterdam, 1992, 513–526.
(with M. Cavani), Bifurcations in a predator-prey model with memory and diffusion, Proc. Int. Conf. Diff. Equat. (Barcelona, 1991), Vol. I, World Sci. Publ., River Edge, NJ, 1993, 379–384.
(with M. Cavani), Bifurcations in a predator-prey model with memory and diffusion: I. Andronov-Hopf bifurcation, Acta Math. Hungar., 63 (1994), 213–229.
(with M. Cavani), Bifurcations in a predator-prey model with memory and diffusion: II. Turing bifurcation, Acta Math. Hungar., 63 (1994), 375–393.
On the distribution of capital and labour in a closed economy, Proc. Int. Conf. Applied Analysis (Hanoi, 1993), South-East Asian Bull. Math., 19 (1995), 27–36.
Spatial inhomogenity due to Turing bifurcation in an economy, Dynamic Systems and Applications (Atlanta, 1995), Vol. II, Dynamic Publishers, Atlanta, 1996, 153–166.
Two ways of modelling cross-diffusion, Proc. 2nd World Congress Nonlin. Analysts (Athens, 1996), Nonlin. Anal., 30 (1997), 1225–1233.
(with J. R. Graef and C. Qian), Asymptotic periodicity of delay differential equations, J. Math. Anal. Appl., 226 (1998), 150–165.
Comparison of different ways of modeling cross-diffusion, Diff. Equat. Dyn. Systems. 7 (1999), 121–137.
(with Z. Horvath and D. Meyer), The three-dimensional dynamics of a two-sector growth model, Szigma, 30 (1999), 197–207 (in Hungarian).
(with P. Van den Driessche and M. L. Zeeman), Bounding the number of cycles of O.D.E.s in ℝn, Proc. Amer. Math. Soc., 129 (2001), 443–449.
On time-periodic patterns, Nonlin. Anal., 44 (2001), 669–678.
On the stability of stationary age distributions, Appl. Math. Comp., 131 (2002), 107–123.
The result of even allocation of funds for postgraduate training, Ann. Univ. Sci. Budapest, Sect. Math., 44 (2002), 193–197.
(with A. Bocsó), Political and economic rationality leads to velcro bifurcation, Appl. Math. Comp., 140 (2003), 381–389.
(with S. Aly), Bifurcations in a predator-prey model in patchy environment with diffusion, Nonlin. Anal. Real World Appl., 5 (2004), 519–526.
(with S. Aly), Competition in patchy environment with cross diffusion, Nonlin. Anal. Real World Appl., 5 (2004), 589–595.
(with S. Aly), Bifurcations in a predator-prey model with cross diffusion, Ann. Univ. Sci. Budapest, Sect. Math., 47 (2004), 35–45.
(with S. Aly), Prey-predator in patchy environment with cross diffusion, Diff. Equat. Dyn. Systems, 13 (2005), 311–321.
(with J. Dias Ferreira and P. C. C. Tabares), Degenerate center in a predator-prey system with memory, Ann. Univ. Sci. Budapest, Sect. Comp., 25 (2005), 53–65.
(with E. Saez and I. Szántó, Velcro bifurcation in competition models with generalized Holling functional response, Miskolc Math. Notes, 6(2005), 185–195.
(with K. Kiss and S. Kovács), Qualitative behaviour of a ratio-dependent predator-prey system, Nonlin. Anal Real World Appl., in print.
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Miklós Farkas Obituary. Period Math Hung 56, 1–9 (2008). https://doi.org/10.1007/s10998-008-5001-4
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DOI: https://doi.org/10.1007/s10998-008-5001-4