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Journal articles on the topic 'Continuous or discrete homogenization'

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Author: Grafiati

Published: 8 June 2024

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1

Gottwald, Georg A., and Ian Melbourne. "Homogenization for deterministic maps and multiplicative noise." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 469, no. 2156 (August 8, 2013): 20130201. http://dx.doi.org/10.1098/rspa.2013.0201.

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A recent paper of Melbourne & Stuart (2011 A note on diffusion limits of chaotic skew product flows. Nonlinearity 24 , 1361–1367 (doi:10.1088/0951-7715/24/4/018)) gives a rigorous proof of convergence of a fast–slow deterministic system to a stochastic differential equation with additive noise. In contrast to other approaches, the assumptions on the fast flow are very mild. In this paper, we extend this result from continuous time to discrete time. Moreover, we show how to deal with one-dimensional multiplicative noise. This raises the issue of how to interpret certain stochastic integrals; it is proved that the integrals are of Stratonovich type for continuous time and neither Stratonovich nor Itô for discrete time. We also provide a rigorous derivation of super-diffusive limits where the stochastic differential equation is driven by a stable Lévy process. In the case of one-dimensional multiplicative noise, the stochastic integrals are of Marcus type both in the discrete and continuous time contexts.

2

Nassar, H., A. Lebée, and L. Monasse. "Curvature, metric and parametrization of origami tessellations: theory and application to the eggbox pattern." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 473, no. 2197 (January 2017): 20160705. http://dx.doi.org/10.1098/rspa.2016.0705.

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Origami tessellations are particular textured morphing shell structures. Their unique folding and unfolding mechanisms on a local scale aggregate and bring on large changes in shape, curvature and elongation on a global scale. The existence of these global deformation modes allows for origami tessellations to fit non-trivial surfaces thus inspiring applications across a wide range of domains including structural engineering, architectural design and aerospace engineering. The present paper suggests a homogenization-type two-scale asymptotic method which, combined with standard tools from differential geometry of surfaces, yields a macroscopic continuous characterization of the global deformation modes of origami tessellations and other similar periodic pin-jointed trusses. The outcome of the method is a set of nonlinear differential equations governing the parametrization, metric and curvature of surfaces that the initially discrete structure can fit. The theory is presented through a case study of a fairly generic example: the eggbox pattern. The proposed continuous model predicts correctly the existence of various fittings that are subsequently constructed and illustrated.

3

Wei, Nan, Hongling Ye, Xing Zhang, Jicheng Li, and Boshuai Yuan. "Vibration Characteristics Research of Sandwich Structure with Octet-truss Lattice Core." Journal of Physics: Conference Series 2125, no. 1 (November 1, 2021): 012059. http://dx.doi.org/10.1088/1742-6596/2125/1/012059.

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Abstract Lattice sandwich beams are often subjected to vibrations when they are used. The aim of this study was to explore the vibration characteristics of the octet-truss lattice core sandwich beam by translating discrete octet-truss core to the continuous homogenization material. The natural frequencies of which are obtained by theoretical calculation and numerical simulation. The theoretical solutions are in good agreement with the numerical results. It demonstrates that the theoretical approach is effective to compute the natural frequency. Furthermore, the influences of truss member radius and thin sheets ply on the natural frequencies are also discussed. The outcomes indicate that the octet-truss lattice core sandwich beam’s natural frequencies are controlled via selecting the appropriate truss member radius and the face sheets thickness.

4

Gomes, Diogo A., and Xianjin Yang. "The Hessian Riemannian flow and Newton’s method for effective Hamiltonians and Mather measures." ESAIM: Mathematical Modelling and Numerical Analysis 54, no. 6 (September 16, 2020): 1883–915. http://dx.doi.org/10.1051/m2an/2020036.

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Effective Hamiltonians arise in several problems, including homogenization of Hamilton–Jacobi equations, nonlinear control systems, Hamiltonian dynamics, and Aubry–Mather theory. In Aubry–Mather theory, related objects, Mather measures, are also of great importance. Here, we combine ideas from mean-field games with the Hessian Riemannian flow to compute effective Hamiltonians and Mather measures simultaneously. We prove the convergence of the Hessian Riemannian flow in the continuous setting. For the discrete case, we give both the existence and the convergence of the Hessian Riemannian flow. In addition, we explore a variant of Newton’s method that greatly improves the performance of the Hessian Riemannian flow. In our numerical experiments, we see that our algorithms preserve the non-negativity of Mather measures and are more stable than related methods in problems that are close to singular. Furthermore, our method also provides a way to approximate stationary MFGs.

5

Josnin, Jean-Yves, Séverin Pistre, and Claude Drogue. "Modélisation d'un système karstique complexe (bassin de St-Chaptes, Gard, France) : un outil de synthèse des données géologiques et hydrogéologiques." Canadian Journal of Earth Sciences 37, no. 10 (October 1, 2000): 1425–45. http://dx.doi.org/10.1139/e00-056.

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Numerous software packages allow the efficient modeling of the hydrodynamic behaviour of aquifers in continuous media. To study pressure transfer in discontinuous media like karsts, the black-box models are restrictive and the models that consider discrete conduit networks are unsuitable for reservoir scale. We show that the utilization of a continuous media model can lead to useful results, even in the case of complex systems, but needs to be adapted to karst specificity. The problem is approached by studying a hydrogeological system located in the Mediterranean Languedoc region: the St-Chaptes basin. This system consists of three superposed aquifers included in four different stratigraphic series. The main aquifer is a karst formation in contact with two other karst formations that belong to different hydrogeologic systems. Considering geological data in addition to hydrological data and with the hypothesis of a relative homogenization of the karst's hydraulic behaviour on a large spatial scale for daily to monthly increments, the model that takes into account the relations with the other aquifers allows (i) a preliminary identification of the main heterogeneities inside the reservoir; (ii) the location of barriers and low-permeability zones that isolate some parts of the aquifer; (iii) the observation of a curious behaviour of the piezometric levels in the confined zones of the aquifer; and (iv) the characterization of the exchanges with the other low-volume but existing aquifers.

6

Amaro-Mellado, José Lázaro, and Dieu Tien Bui. "GIS-Based Mapping of Seismic Parameters for the Pyrenees." ISPRS International Journal of Geo-Information 9, no. 7 (July 17, 2020): 452. http://dx.doi.org/10.3390/ijgi9070452.

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In the present paper, three of the main seismic parameters, maximum magnitude -Mmax, b-value, and annual rate -AR, have been studied for the Pyrenees range in southwest Europe by a Geographic Information System (GIS). The main aim of this work is to calculate, represent continuously, and analyze some of the most crucial seismic indicators for this belt. To this end, an updated and homogenized Poissonian earthquake catalog has been generated, where the National Geographic Institute of Spain earthquake catalog has been considered as a starting point. Herein, the details about the catalog compilation, the magnitude homogenization, the declustering of the catalog, and the analysis of the completeness, are exposed. When the catalog has been produced, a GIS tool has been used to drive the parameters’ calculations and representations properly. Different grids (0.5 × 0.5° and 1 × 1°) have been created to depict a continuous map of these parameters. The b-value and AR have been obtained that take into account different pairs of magnitude–year of completeness. Mmax has been discretely obtained (by cells). The analysis of the results shows that the Central Pyrenees (mainly from Arudy to Bagnères de Bigorre) present the most pronounced seismicity in the range.

7

Pradel, F., and K. Sab. "Homogenization of discrete media." Le Journal de Physique IV 08, PR8 (November 1998): Pr8–317—Pr8–324. http://dx.doi.org/10.1051/jp4:1998839.

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8

Etoughe, M. Betoue, and G. Panasenko. "Partial homogenization of discrete models." Applicable Analysis 87, no. 12 (December 2008): 1425–42. http://dx.doi.org/10.1080/00036810802378638.

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9

Braides, Andrea, Valeria Chiadò Piat, and Andrey Piatnitski. "Homogenization of Discrete High-Contrast Energies." SIAM Journal on Mathematical Analysis 47, no. 4 (January 2015): 3064–91. http://dx.doi.org/10.1137/140975668.

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10

Caillerie, Denis, Ayman Mourad, and Annie Raoult. "Discrete Homogenization in Graphene Sheet Modeling." Journal of Elasticity 84, no. 1 (March 30, 2006): 33–68. http://dx.doi.org/10.1007/s10659-006-9053-5.

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11

Ricker, Sarah, Andreas Menzel, and Paul Steinmann. "Towards the computational homogenization of discrete microstructures." PAMM 7, no. 1 (December 2007): 4080021–22. http://dx.doi.org/10.1002/pamm.200700583.

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12

PANASENKO, GRIGORY. "THE PARTIAL HOMOGENIZATION: CONTINUOUS AND SEMI-DISCRETIZED VERSIONS." Mathematical Models and Methods in Applied Sciences 17, no. 08 (August 2007): 1183–209. http://dx.doi.org/10.1142/s0218202507002248.

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The partial homogenization is a new method for the treatment of the boundary layers in the homogenization theory. It keeps the initial formulation near the boundary, passes to the high order homogenization at some distance from the boundary and prescribes the asymptotically precise junction conditions between the homogenized and the heterogeneous models at the interface. This method is related to the method of asymptotic partial domain decomposition MAPDD (see G. Panasenko, Method of asymptotic partial decomposition of domain, Math. Mod. Meth. Appl. Sci.8 (1998) 139–156). The partial homogenization (as well as the MAPDD) can be interpreted as a multi-scale model coupling the homogenized (macroscopic) description in the internal main part of the domain and the microscopic zoom in the domain of the location of the boundary layers. The semi-discretized partial homogenization uses some high order finite element projection in the homogenized subdomain.

13

NGUYEN, VINH PHU, MARTIJN STROEVEN, and LAMBERTUS JOHANNES SLUYS. "MULTISCALE CONTINUOUS AND DISCONTINUOUS MODELING OF HETEROGENEOUS MATERIALS: A REVIEW ON RECENT DEVELOPMENTS." Journal of Multiscale Modelling 03, no. 04 (December 2011): 229–70. http://dx.doi.org/10.1142/s1756973711000509.

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This paper reviews the recent developments in the field of multiscale modelling of heterogeneous materials with emphasis on homogenization methods and strain localization problems. Among other topics, the following are discussed (i) numerical homogenization or unit cell methods, (ii) continuous computational homogenization for bulk modelling, (iii) discontinuous computational homogenization for adhesive/cohesive crack modelling and (iv) continuous-discontinuous computational homogenization for cohesive failures. Different boundary conditions imposed on representative volume elements are described. Computational aspects concerning robustness and computational cost of multiscale simulations are presented.

14

Ali, Mohamad Hasan, and Julius M. Zelmanowitz. "Discrete Implies Continuous." Journal of Algebra 183, no. 1 (July 1996): 186–92. http://dx.doi.org/10.1006/jabr.1996.0213.

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15

Kwon, Y. W., and C. Manthena. "Homogenization technique of discrete atoms into smeared continuum." International Journal of Mechanical Sciences 48, no. 12 (December 2006): 1352–59. http://dx.doi.org/10.1016/j.ijmecsci.2006.07.014.

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16

Tollenaere, H., and D. Caillerie. "Continuous modeling of lattice structures by homogenization." Advances in Engineering Software 29, no. 7-9 (August 1998): 699–705. http://dx.doi.org/10.1016/s0965-9978(98)00034-9.

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17

Xia, Yuanqing, Zhihong Deng, Li Li, and Xiumei Geng. "A new continuous-discrete particle filter for continuous-discrete nonlinear systems." Information Sciences 242 (September 2013): 64–75. http://dx.doi.org/10.1016/j.ins.2013.04.030.

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18

BRAIDES, ANDREA, and MARGHERITA SOLCI. "INTERFACIAL ENERGIES ON PENROSE LATTICES." Mathematical Models and Methods in Applied Sciences 21, no. 05 (May 2011): 1193–210. http://dx.doi.org/10.1142/s0218202511005295.

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In this paper we prove a homogenization theorem for interfacial discrete energies defined on an a-periodic Penrose tiling in ℝ2. A general result on the homogenization of surface energies cannot be directly adapted to this case; the existence of the limit interfacial energy is therefore proved by showing some refined "quasi-periodic" properties of the tilings.

19

Neukamm, Stefan, Mathias Schäffner, and Anja Schlömerkemper. "Stochastic Homogenization of Nonconvex Discrete Energies with Degenerate Growth." SIAM Journal on Mathematical Analysis 49, no. 3 (January 2017): 1761–809. http://dx.doi.org/10.1137/16m1097705.

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20

Dos Reis, F., and J. F. Ganghoffer. "Equivalent mechanical properties of auxetic lattices from discrete homogenization." Computational Materials Science 51, no. 1 (January 2012): 314–21. http://dx.doi.org/10.1016/j.commatsci.2011.07.014.

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21

Alfaro, M. V. Cid, A. S. J. Suiker, C. V. Verhoosel, and R. de Borst. "Computational homogenization of discrete fracture in fibre-epoxy systems." International Journal of Material Forming 2, S1 (August 2009): 931–34. http://dx.doi.org/10.1007/s12289-009-0593-7.

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22

Morduchow, Morris. "Discrete and Continuous Compounding." American Mathematical Monthly 92, no. 10 (December 1985): 734. http://dx.doi.org/10.2307/2323232.

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23

Maksimov, Vladimir Petrovich. "Continuous-discrete dynamic models." Ufimskii Matematicheskii Zhurnal 13, no. 3 (2021): 95–103. http://dx.doi.org/10.13108/2021-13-3-95.

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24

AKATSUKA, Takeaki, Nobuo FURUMATSU, and Hirokazu NISHITANI. "Combined Continuous-Discrete Simulation." Transactions of the Society of Instrument and Control Engineers 34, no. 3 (1998): 247–53. http://dx.doi.org/10.9746/sicetr1965.34.247.

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25

Morduchow, Morris. "Discrete and Continuous Compounding." American Mathematical Monthly 92, no. 10 (December 1985): 734–35. http://dx.doi.org/10.1080/00029890.1985.11971726.

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26

Bowins, Brad. "Depression: Discrete or Continuous?" Psychopathology 48, no. 2 (December 13, 2014): 69–78. http://dx.doi.org/10.1159/000366504.

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27

Böckenholt, Ulf, Eric Bradlow, Wes Hutchinson, Ramya Neelamegham, Prashant Malaviya, Deborah Roedder John, Kent Grayson, Jan-Benedict Steenkamp, Greg Allenby, and Sachin Gupta. "Continuous and Discrete Variables." Journal of Consumer Psychology 10, no. 1-2 (2001): 37–53. http://dx.doi.org/10.1207/s15327663jcp1001&2_04.

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28

Hall, Randolph W. "Discrete models/continuous models." Omega 14, no. 3 (January 1986): 213–20. http://dx.doi.org/10.1016/0305-0483(86)90040-x.

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29

Stein, Oliver, Jan Oldenburg, and Wolfgang Marquardt. "Continuous reformulations of discrete–continuous optimization problems." Computers & Chemical Engineering 28, no. 10 (September 2004): 1951–66. http://dx.doi.org/10.1016/j.compchemeng.2004.03.011.

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30

STEFANOU, IOANNIS, and JEAN SULEM. "THREE-DIMENSIONAL COSSERAT CONTINUUM MODELING OF FRACTURED ROCK MASSES." Journal of Multiscale Modelling 02, no. 03n04 (September 2010): 217–34. http://dx.doi.org/10.1142/s1756973710000424.

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The behavior of rock masses is influenced by the existence of discontinuities, which divide the rock in joint blocks making it an inhomogeneous anisotropic material. From the mechanical point of view, the geometrical and mechanical properties of the rock discontinuities define the mechanical properties of the rock structure. In the present paper we consider a rock mass with three joint sets of different dip angle, dip direction, spacing and mechanical properties. The dynamic behavior of the discrete system is then described by a continuum model, which is derived by homogenization. The homogenization technique applied here is called generalized differential expansion homogenization technique and has its roots in Germain's (1973) formulation for micromorphic continua. The main advantage of the method is the avoidance of the averaging of the kinematic quotients and the derivation of a continuum that maps exactly the degrees of freedom of the discrete system through a one-to-one correspondence of the kinematic measures. The derivation of the equivalent continuum is based on the identification for any virtual kinematic field of the power of the internal forces and of the kinetic energy of the continuum with the corresponding quantities of the discrete system. The result is an anisotropic three-dimensional Cosserat continuum.

31

Fichtner, Andreas, and Shravan M. Hanasoge. "Discrete wave equation upscaling." Geophysical Journal International 209, no. 1 (January 17, 2017): 353–57. http://dx.doi.org/10.1093/gji/ggx016.

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Abstract We present homogenization technique for the uniformly discretized wave equation, based on the derivation of an effective equation for the low-wavenumber component of the solution. The method produces a down-sampled, effective medium, thus making the solution of the effective equation less computationally expensive. Advantages of the method include its conceptual simplicity and ease of implementation, the applicability to any uniformly discretized wave equation in 1-D, 2-D or 3-D, and the absence of any constraints on the medium properties. We illustrate our method with a numerical example of wave propagation through a 1-D multiscale medium and demonstrate the accurate reproduction of the original wavefield for sufficiently low frequencies.

32

Arenz, Christian, Daniel Burgarth, and Robin Hillier. "Dynamical decoupling and homogenization of continuous variable systems." Journal of Physics A: Mathematical and Theoretical 50, no. 13 (March 3, 2017): 135303. http://dx.doi.org/10.1088/1751-8121/aa6017.

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33

Zhao, Hongwei, Kai Long, and Z. D. Ma. "Homogenization Topology Optimization Method Based on Continuous Field." Advances in Mechanical Engineering 2 (January 2010): 528397. http://dx.doi.org/10.1155/2010/528397.

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34

Bryantsev, P. Yu, V. S. Zolotorevskiy, and V. K. Portnoy. "The Effect of Heat Treatment and Mn, Cu and Cr Additions on the Structure of Ingots of Al-Mg-Si-Fe Alloys." Materials Science Forum 519-521 (July 2006): 401–6. http://dx.doi.org/10.4028/www.scientific.net/msf.519-521.401.

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Phase transformations in 6XXX alloys with Mn, Cu and Cr additions have been studied in the process of homogenization annealing at different temperatures. The continuous cooling transformation diagrams of decomposition of solid solution during the cooling of ingots from the homogenization temperature have been plotted. The effect of the cooling rate after homogenization on the properties of ingots during extrusion has been studied.

35

Mazzola, Claudio. "Can discrete time make continuous space look discrete?" European Journal for Philosophy of Science 4, no. 1 (September 10, 2013): 19–30. http://dx.doi.org/10.1007/s13194-013-0072-3.

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36

Damlamian, Alain, and Klas Pettersson. "Homogenization of oscillating boundaries." Discrete and Continuous Dynamical Systems 23, no. 1/2 (September 2008): 197–219. http://dx.doi.org/10.3934/dcds.2009.23.197.

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37

Frénod, Emmanuel. "Homogenization-based numerical methods." Discrete and Continuous Dynamical Systems - Series S 9, no. 5 (October 2016): i—ix. http://dx.doi.org/10.3934/dcdss.201605i.

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38

Wang, Jiaolong, Dexin Zhang, and Xiaowei Shao. "New version of continuous–discrete cubature Kalman filtering for nonlinear continuous–discrete systems." ISA Transactions 91 (August 2019): 174–83. http://dx.doi.org/10.1016/j.isatra.2019.01.016.

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39

Braides, Andrea, Marco Cicalese, and Matthias Ruf. "Continuum limit and stochastic homogenization of discrete ferromagnetic thin films." Analysis & PDE 11, no. 2 (January 1, 2018): 499–553. http://dx.doi.org/10.2140/apde.2018.11.499.

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40

OKUMURA, Dai, Nobutada OHNO, and Yoshihiro KATAGIRI. "Formulation of a Homogenization Theory for Discrete Dislocation Dynamics Analysis." Journal of the Society of Materials Science, Japan 59, no. 2 (2010): 149–56. http://dx.doi.org/10.2472/jsms.59.149.

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41

Lemarchand, C., B. Devincre, and L. P. Kubin. "Homogenization method for a discrete-continuum simulation of dislocation dynamics." Journal of the Mechanics and Physics of Solids 49, no. 9 (September 2001): 1969–82. http://dx.doi.org/10.1016/s0022-5096(01)00026-6.

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42

Goda, Ibrahim, Mohamed Assidi, and Jean-François Ganghoffer. "Equivalent mechanical properties of textile monolayers from discrete asymptotic homogenization." Journal of the Mechanics and Physics of Solids 61, no. 12 (December 2013): 2537–65. http://dx.doi.org/10.1016/j.jmps.2013.07.014.

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43

Droździel, Paweł, Tetiana Vitenko, Viktor Voroshchuk, Sergiy Narizhnyy, and Olha Snizhko. "Discrete-Impulse Energy Supply in Milk and Dairy Product Processing." Materials 14, no. 15 (July 27, 2021): 4181. http://dx.doi.org/10.3390/ma14154181.

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The efficient use of supplied energy is the basis of the discrete-impulse energy supply (DIES) concept. In order to explore the possibility of using DIES to intensify the hydromechanical processes, the emulsification of milk fat (homogenization of milk, preparation of spreads) and, in particular, the processing of cream cheese masses, were studied. Whole non-homogenized milk, fat emulsions, and cream cheese mass were the object of investigation. To evaluate the efficiency of milk homogenization, the homogenization coefficient change was studied, which was determined by using the centrifugation method, as it is the most affordable and accurate one. To provide the proper dispersion of the milk emulsion, six treatment cycles must be carried out under the developed cavitation mode in a static-type apparatus, here resulting in a light grain-like consistency, and exhibiting the smell of pasteurized milk. The emulsions were evaluated according to the degree of destabilization, resistance and dispersion of the fat phase. On the basis of the obtained data with respect to the regularities of fat dispersion forming in the rotor-type apparatus, the proper parameters required to obtain technologically stable fat emulsion spreads, possessing a dispersion and stability similar to those of plain milk creams, were determined. It was determined that under the DIES, an active dynamic effect on the milk globules takes place. The rheological characteristics of cheese masses were evaluated on the basis of the effective change in viscosity. The effect of the mechanical treatment on the structure of the cheese masses was determined.

44

Díaz Martín, Rocío, Ivan Medri, and Ursula Molter. "Continuous and discrete dynamical sampling." Journal of Mathematical Analysis and Applications 499, no. 2 (July 2021): 125060. http://dx.doi.org/10.1016/j.jmaa.2021.125060.

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45

Goldin, Owen. "The Continuous and the Discrete." Ancient Philosophy 15, no. 1 (1995): 277–83. http://dx.doi.org/10.5840/ancientphil199515161.

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46

Demyanovich, Yuri, and Le Thi Nhu Bich. "Discrete and Continuous Wavelet Expansions." WSEAS TRANSACTIONS ON MATHEMATICS 21 (February 23, 2022): 58–67. http://dx.doi.org/10.37394/23206.2022.21.9.

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This paper proposes a new approach to the construction of wavelet decomposition, which is suitable for processing a wide range of information flows. The proposed approach is based on abstract functions with values in linear topological spaces. It is defined by embedded spaces and their projections. The proposed approach allows for adaptive ways of decomposition for the initial flow depending on the speed changes of the last one. The initial information flows can be real number flows, flows of complex and p-adic numbers, as well as flows of (finite or infinite) vectors, matrices, etc. The result is illustrated with examples of spline-wavelet decompositions of discrete flows, and also with the example of the decomposition of a continuous flow.

47

Anapolitanos, D. A. "The Continuous and The Discrete." Philosophical Inquiry 13, no. 1 (1991): 1–24. http://dx.doi.org/10.5840/philinquiry1991131/21.

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48

Balaji, Bhashyam. "Continuous-Discrete Path Integral Filtering." Entropy 11, no. 3 (August 17, 2009): 402–30. http://dx.doi.org/10.3390/e110300402.

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49

Mazzoni, Thomas. "Fast continuous-discrete DAF-filters." Journal of Time Series Analysis 33, no. 2 (July 27, 2011): 193–210. http://dx.doi.org/10.1111/j.1467-9892.2011.00751.x.

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50

Béné, Christophe, and Claude Lobry. "Discrete Versus Continuous Controlled System." Journal of Biological Systems 06, no. 02 (June 1998): 127–57. http://dx.doi.org/10.1142/s0218339098000121.

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Because decision making processes involve costly mechanisms, they seldom are implemented continuously but instead take place at discrete time intervals. The question is then: what is the impact of this process discreteness on the systems dynamics? This problem is set here in the context of fisheries. Through a very simple though realistic model representing a shrimp fishery, we show that a discrete decision making process may lead to dynamics that differ completely from those obtained with a continuous process. For this purpose, we consider the interaction between a shrimp stock and the exploiting fleet. We then focus on the decision process that governs the allocation of the fleet fishing effort between the two stages of this stock: the young adults living near the coast and the mature adults located offshore. We first analyze the behaviour of the system when the discreteness in the decision making is not accounted for. In that case, the system turns out to be globally stable. We then identify the behaviour of the system when the decision process is discretised. In that case the solutions of the system yield sustained periodic oscillations. Our conclusion is that discreteness which is known to occur in decision making processes of most anthropic systems should be taken into account, especially in studies aiming precisely at investigating the dynamics of such systems.