Alex Potapov

Publications

Book

G.G. Malinetskii, A.B. Potapov. Modern problems of nonlinear dynamics, 2nd ed. Moscow, URSS publishers, 2000, 335p. (in Russian ).

Journal Articles

·   A. PotapovH. Rajakaruna, Allee threshold and stochasticity in biological invasions: Colonization time at low propagule pressure. Journal of Theoretical Biology (2013).
·   A. Potapov, E. Merrill, M. Pybus, D. Coltman, M.A. Lewis. Chronic wasting disease: Possible transmission mechanisms in
deer. Ecological Modelling 250 (2013) 244-257.
·   H. Rajakaruna, A. Potapov, M.A. Lewis.  Impact of stochasticity in immigration and reintroductions on colonizing and declining populations.  Theoretical Population Biology (2013).
·   A. Potapov, E. Merrill, M.A. Lewis. Wildlife disease elimination and density dependence. Proc. R. Soc. B 279 (2012) 3139-3145 .
·   A. Potapov, J. Muirhead, N. Yan, S. Lele, M. Lewis. Models of lake invasibility by Bythotrephes longimanus, a non-indigenous zooplankton. Biological Invasions 13(11) (2011) 2459-2476.
·   A. Potapov, J.R. Muirhead, S.R. Lele, M.A. Lewis. Stochastic gravity models for modeling lake invasions. Ecological Modelling 222 (2011) 964–972.
·   D. Finnoff, A. Potapov, M.A. Lewis. Control and the management of a spreading invader. Resource and Energy Economics 32 (2010) 534–550.
·   D. Finnoff, A. Potapov,  M.A. Lewis. Second best policies in invasive species management: When are they good enough?  In: Bioinvasions & Globalization. Ecology, Economics, Management, and Policy. C. Perrings, H. Mooney, M. Williamson, eds. Oxford University Press 2010, Oxford, UK, pp. 110-126.
·   A. Potapov. Stochastic model of lake system invasion and its optimal control: neurodynamic programming as a solution method. Nat. Res. Mod., 22, issue 2 (2009) 257288.
·   A.B. Potapov, M.A. Lewis. Allee effect and control of lake system invasion. Bull. Math. Biol. 70 (2008), 1371–1397.
·   Nelson, W.A., Potapov, A., Lewis, M.A., Hundsdoerfer, A.E., He, F.  Balancing ecological complexity in predictive models: a reassessment of risk models in the mountain pine beetle system. Journal of Applied Ecology 45 (2008) 248-257.
·   E.G. Noonburg, L.A. Newman, M. Lewis, R.L. Crabtree, A.B. Potapov. Sequential decision-making in a variable environment: Modeling elk
movement in Yellowstone National Park as a dynamic game
. Theoretical Population Biology 71 (2007) 182–195.
·   A.B. Potapov, M.A. Lewis., D. Finnoff. Optimal Control of Biological Invasions in Lake Networks. Nat. Res. Mod., (2007), 20(3) 351-379.
·    A.B. Potapov, T. Hillen. Metastability in chemotaxis models . J. Dynamics Diff. Eqs., 2005.
·    A.B. Potapov, M. Lewis. Climate and competition: the effect of moving range boundaries on habitat invisibility . Bull. Math. Biol., (2004), 66, 975–1008.
·    T. Hillen, A. Potapov. The one-dimensional chemotaxis model: global existence and asymptotic profile. Math. Methods in Appl. Sci., 27 (2004), 27, 1783–1801.
·    A.B. Potapov, M.K. Ali. Convergence of reinforcement learning algorithms and acceleration of learning . Phys. Rev. E, 67 (2003), 026706.
·    A.B. Potapov, M.K. Ali. Neural networks for estimating intrinsic dimension . Phys. Rev. E, 65 (2002), 046212.
·    A.B. Potapov, M.K. Ali. Nonlinear dynamics and chaos in information processing neural networks . Differential Equations and Dynamical Systems, Vol.9, Nos. 3&4, (2001) 259-319. (То же по-русски )
·    A.B. Potapov, M.K. Ali. Storing patterns in Hamiltonian neural networks. Int. J. Mod. Phys. C, 12, 8 (2001) 1217-1228.
·    A.B. Potapov, M.K. Ali. Pattern Recognition with Hamiltonian Dynamics. Int. J. Mod. Phys. C, 12, 5 (2001) 751-758.
·    A.B. Potapov, M.K. Ali. Chaotic neural control . Phys. Rev. E, 63 (2001), 046215.
·    A.B. Potapov, M.K. Ali. Robust chaos in neural networks . Phys. Lett. A, 277 (2000) 310-322.
·    A.B. Potapov, M.K. Ali. Learning, exploration and chaotic policies. Int. J. Mod. Phys. C, 11, 7 (2000) 1455- 1464.
·    A.B. Potapov, J. Kurths. Correlation integral as a tool for distinguishing between dynamics and statistics in time series data . Physica D, 120 (1998) 369-385.
·    G.G. Malinetskii, A.B. Potapov. Channels and jokers: neural view of complex dynamics. Izv. VUZ Appl. Nonl. Dynamics, 6 (1998) 18-29.
·    S.V. Ershov, A.B. Potapov. On the concept of Stationary Lyapunov basis . Physica D, 118 (1998) 167-198.
·    A.B. Potapov. Characteristic scales of reconstruction distortions . Int.J.Bifurc.and Chaos, 8 (1998) 835-841.
·    Trofimova, A.B. Potapov, W. Sulis. Collective effects on individual behavior: in search of universality. Int. J. Chaos Theory and Applications, 1998 35-45.
·    S.V. Ershov, A. B. Potapov. On mean field fluctuations in globally coupled logistic-type maps. Physica D, 106 (1997) 9-38.
·    T.S. Akhromeyeva, S.A. Kaschenko, S.P. Kurdyumov, G.G. Malinetskii, N.A. Mitin, A.B. Potapov.  Higher education as an object of mathematical modeling. Phystech Journal, 3 (1997) 115-145.
·    G.G. Malinetskii, A.B. Potapov, I.V. Feldstein. On the possibility of estimating a diffusion coefficient of a medium from observations in a number of points. J. Tech. Phys., 67 (1997) 127-130 (in Russian).
·    A.B. Potapov. Distortions of reconstruction for chaotic attractors . Physica D, 101 (1997) 207-226.
·    G.G. Malinetskii, A.B. Potapov, I.V. Feldstein. New approach to estimating of diffusion coefficient. Izv. VUZ, Applied Nonlinear Dynamics 4 (1997) 82-91 (in Russian).
·    S.V. Ershov, A.B.  Potapov. On mean field fluctuations in globally coupled maps Physica D, 86 (1995) 523-558.
·    I.B. Bokolishvily, S.A. Kaschenko, G.G. Malinetskii, A.B. Potapov. Complex ordering and stochastic oscillations in a class of reaction-diffusion systems with small diffusion. J. Nonlinear Sci., 4 (1994) 545-562.
·    G.G. Malinetskii, A.B. Potapov, G.Z. Tsertsvadze. Qualitative features of diffusion-induced chaos. J. Comput. Math. Math. Phys., 34 (1994) 554-563 (in Russian).
·    I.A. Kostylev, G.G. Malinetskii, A.B. Potapov Order parameters in a Hopfield neural network. Comp. Maths. Math. Phys., 34 (1994) 1493-1500.
·    G.G. Malinetskii, A.B. Potapov, A.I. Rakhmanov. E.B. Rodichev. Limitations of delay reconstruction for chaotic systems with a broad spectrum. Phys. Lett. A, 179 (1993) 15-22.
·    G.G. Malinetskii, A.B. Potapov, A.I. Rakhmanov. Limitations of delay reconstruction for chaotic dynamical systems . Phys. Rev. E, 48 (1993) 904-912.
·    S.V. Ershov, A.B. Potapov. Macrodynamics: large scale structures in turbulent media. J. Stat. Phys., 69 (1992) 763-780.
·    I.B. Bokolishvili, A.V. Kim, G.G. Malinetskii, A.S. Petrosyan, A.B. Potapov. Dynamics of a nonequilibrium discharge in a covering cylindrical wave under the condition of intensive gas heating. Physica Scripta, 45 (1992) 91-99.
·    T.S. Akhromeyeva, G.G. Malinetskii, A.B. Potapov, G.Z. Tsertsvadze. New properties of quasiperiodic solutions of the complex Ginzburg-Landau equation.  Bifurc. and Chaos in Appl.  Sci.  Engin. 2 (1992) 955-972.
·    S.V. Ershov, A.B. Potapov. On the nature of nonchaotic turbulence. Phys. Lett. A, 167 (1992) 60-64.
·    G.G. Malinetskii, A.B. Potapov, S.M. Gizzatulina, A.A. Ruzmaikin, V.D. Rukavishnikov. Dimension of geomagnetic attractor from the data on length of day variations. Phys. Earth Plan. Inter., 59 (1990) 170-181.
·    G.G. Malinetskii, A.B. Potapov, V.G. Priimak. On the possibility of describing turbulent flows of a viscous fluid by a finite-dimensional attractor. Sov. Phys.-Dokl., 36 (1991) 141-144.
·    T.S. Akhromeyeva, G.G. Malinetskii, A.B. Potapov, G.Z. Tsertsvadze. New properties of quasiperiodic solutions of the complex Ginzburg-Landau equation. Sov. Phys-Dokl., 36 (1991) 941-950.
·    S.P. Kurdyumov, G.G. Malinetskii, A.B. Potapov. Approximate studies of symmetric localized structures. Sov. Phys.-Dokl., 35 (1990) 796-799.
·    F.V. Bunkin, N.A. Kirichenko, S.P. Kurdyumov, A.B. Potapov, A.A. Samarskii. Thermal-diffusion oscillations in a gas mixture in a field of laser radiation. Sov. Phys.-Dokl., 33 (1988) 944-946.
·    G.G. Malinetskii, A.B. Potapov. Estimating dimensions of strange attractors. J. Comput. Math. & Math. Phys., 28 (1988) 1021-1036 (in Russian).
·    S.P. Kurdyumov, G.G. Malinetskii, A.B. Potapov, A.A. Samarskii. Complex multidimensional structures of nonlinear medium. J. Comput. Math. & Math. Phys., 28 (1986) 1189-1205 (in Russian).
·    S.P. Kurdyumov, E.S. Kurkina, A.B. Potapov, A.A. Samarskii. The architecture of multidimensional thermal structures. Sov. Phys.-Dokl., 29 (1984) 106-108.


 

Book chapters

1. A.B. Potapov. Are the RR-interval data appropriate to study the dynamics of heart? In: Nonlinear analysis of physiological data. H. Kantz, J. Kurths, G. Mayer-Kress, eds., Springer, 1998, 117-127.
2. S.P. Kurdyumov, G.G. Malinetskii, A.B. Potapov. Nonstationary structures, dynamical chaos, cellular automata. Progress in Synergetics, Moscow, Nauka, 1996, 95-164 (in Russian).
3. G.G. Malinetskii, A.B. Potapov. Nonlinearity. New problems, new possibilities. Progress in Synergetics, Moscow, Nauka, 1996, 165-190 (in Russian).
4. S.P. Kurdyumov, G.G. Malinetskii, A.B. Potapov, A.A. Samarskii. Structures in nonlinear media. In: Computers and Nonlinear Phenomena, Nauka, Moscow, 1988, 5-43 (in Russian).
5. T.S. Akhromeyeva, S.P. Kurdyumov, G.G. Malinetskii, A.B. Potapov, A.A. Samarskii. New types of order and stochastic regimes in nonlinear media. In: Thermodynamics and pattern formation in biology, Berlin: W.de Gruyter, 1988, 35-56.
 
 
 

 Preprints

1. G.G. Malinetskii, A.B. Potapov.  Channels and jokers: towards new methods of predicting a complex system behavior. KIAM Preprint, 1998, #32, 20p. (in Russian).
2. A.B. Potapov, J. Kurths. Could a time series be processed as deterministic? Correlation integral as a criterion. KIAM Preprint, 1997, #35, 28p.
3. G.G. Malinetskii, N.A. Mitin, A.B. Potapov, I.N. Trofimova. Description of ensembles with variable structure. New models of mathematical psychology. KIAM Preprint, 1997, #34, 12p.
4. S.V. Ershov, A.B. Potapov. Pulse neural networks: a bridge between classical neural network models and coupled map lattices. KIAM Preprint, 1996, #10, 13p. (in Russian)
5. G.G. Malinetskii, S.A. Kaschenko, A.B. Potapov, T.S. Akhromeyeva, N.A. Mitin, M.S. Shakaeva. Modeling of education system. KIAM Preprint, 1995, #100, 48p. (in Russian)
6. G.G. Malinetskii, S.A. Kaschenko, A.B. Potapov, T.S. Akhromeyeva, N.A. Mitin, T.A. Paleeva. Modeling of changes in university education. Medium scale models. KIAM Preprint, 1996, #37, 52p. (in Russian)
7. S.V. Ershov, A.B. Potapov. Dimensions of attractor reconstructions and ordering of nearest neighbors. KIAM Preprint, 1995, #8, 12p. (in Russian).
8. A.B. Potapov. Quality of reconstruction for chaotic attractors and the choice of reconstruction parameters. KIAM Preprint, 1995, #13, 28p. (in Russian).
9. G.G. Malinetskii, A.B. Potapov. Nonlinearity. New problems, new possibilities. KIAM Preprint, 1994, #71, 32p. (in Russian)
10. A.B. Potapov. Curvature, reconstruction from a time series and “natural time” for chaotic dynamical systems. KIAM Preprint, 1993, #11 23p. (in Russian).
11. G.G. Malinetskii, A.B. Potapov, A.I. Rakhmanov. Limitations of attractor `reconstruction for chaotic dynamical systems. KIAM Preprint, 1993, #10 26p. (in Russian)
12. G.G. Malinetskii, I.A. Kostylev, A.B. Potapov. Pattern correlations as the order parameters in neural networks. KIAM Preprint, 1992, #43. 31p. (in Russian)
13. G.G. Malinetskii, A.B. Potapov, G.Z. Tsertsvadze. Study of diffusion-induced chaos. KIAM Preprint, 1992, #46. 35p. (in Russian).
14. A.B. Potapov. FORTRAN-77 full screen access library for the ES-7927 terminal. KIAM Preprint, 1991, #28. 26p. (in Russian)
15. S.V. Ershov, A.B. Potapov. Macrodynamics: large-scale structures in turbulent media. KIAM Preprint, 1991, #122, 19p.
16. G.G. Malinetskii, A.B. Potapov. Geometry of strange attractors and estimation of Lyapunov exponents from a time series. KIAM Preprint, 1991, #13. 28p. (in Russian)
17. A.B. Potapov. Programs for estimating correlation dimension and generalized entropy from a time series. KIAM Preprint, 1991, #13. 28p. (in Russian)
18. T.S. Akhromeyeva, G.G. Malinetskii, A.B. Potapov, G.Z. Tsertsvadze. Periodic and symmetric solutions of Kuramoto-Tsuzuki equation. KIAM Preprint, 1991, #87. 30p. (in Russian).
19. G.G. Malinetskii, A.B. Potapov, V.G. Priimak. Geometric and statistical characteristics of the attractor of Navier-Stokes equations for turbulent flows of viscous fluid in a circular pipe. KIAM Preprint, 1990, #28. 33p. (in Russian).
20. I.B. Bokolishvili, S.A. Kaschenko, G.G. Malinetskii, A.B. Potapov. Local dynamics of some two-component systems with small diffusion. KIAM Preprint, 1990, #47. 33p. (in Russian).
21. I.B. Bokolishvili, S.A. Kaschenko, G.G. Malinetskii, A.B. Potapov. Steady-state regimes in a number of two-component systems with small diffusion. KIAM Preprint, 1989, #142. 26p. (in Russian).
22. I.B. Bokolishvili, A.V. Kim, G.G. Malinetskii, A.B. Potapov, A.S. Petrosyan. Dynamics of non-equilibrium discharge in the field of converging cylindrical wave under intensive gas heating. KIAM Preprint, 1989, #76. 23p. (in Russian).
23. S.M. Gizzatulina, G.G. Malinetskii, A.B. Potapov, A.A. Ruzmaikin, V.D. Rukavishnikov. Dimension of geomagnetic attractor from length of day variations data. KIAM Preprint, 1988, #95. 25p. (in Russian).
24. G.G. Malinetskii, A.B. Potapov. On estimation of dimensions of strange attractors. KIAM Preprint, 1987, #101, 25p. (in Russian)
25. F.V. Bunkin, N.A. Kirichenko, S.P. Kurdyumov, A.B. Potapov, A.A. Samarskii. Autowave processes in gaseous media with thermodiffusion initiated with laser irradiation. KIAM Preprint, 1986, #40. 22p. (in Russian).
26. A.B. Potapov. Obtaining two-dimensional eigenfunctions of the nonlinear medium. KIAM Preprint, 1986, #8, 26p. (in Russian)
27. S.P. Kurdyumov, E.S. Kurkina, A.B. Potapov. Studies of multidimensional architecture of the nonlinear medium eigenfunctions. KIAM Preprint, 1982, #75, 28p. (in Russian).

Conference presentations

1. A. Potapov, M.K. Ali.  Chaotic neural control. In: Workshop on Memory, Delays and Stability, University of Montreal, October 12-15, 2000, p.42-43.
2. G.G. Malinetskii, A.B. Potapov.  Channels and jokers. On new approaches to predicting of the behavior of complex systems. In: V All-Russia Conference “Neurocomputers and Their Applications”, Moscow, Institute of Control Processes RAS, 1999, p.455-458 (in Russian).
3. Potapov A.B., Malinetskii G.G.  Channels and Jokers. New approaches for predicting complex dynamics. In: Abstracts of 5 International School “Chaotic Oscillations and Formation of Structures”, Saratov, October 6–10, 1998, p.51-52.
4. Potapov A.B.  Nonlinear dynamics and time series analysis. In: Abstracts of the Workshop on nonlinear and improperly posed problems, August 17--22, 1998, Kocaeli, Turkey, p. 88-90.
5. A.B.Potapov. Time-series analysis:  when dynamical algorithms can be used Proc. 5 Int.  Specialist Workshop Nonlinear Dynamics of Electronic Systems, Moscow, June 26-27, 1997, 388-393
6. I.V. Feldstein, G.G. Malinetskii, A.B. Potapov The method of association of symbolic sequence with scalar time-series, NDES'97, Moscow, 26-27 June 1997,
7. G.G. Malinetskii, A.B. Potapov, I.V. Feldstein. On estimation of diffusion coefficient from time series. Abstracts of IV Int. conf. Mathematics, Computer, Education, Puschino, 1997, p.159.
8. Potapov A.B.  Characteristic scales of reconstruction distortions. In: Abstracts of International Conference ''Nonlinear dynamics and chaos'', Saratov, July 8–14 1996, p.147.
9. I.B. Bokolishvili, S.A. Kaschenko, G.G. Malinetskii, A.B. Potapov. Complex ordering and stochastic oscillations in some reaction-diffusion systems. In: Mathematical Modeling and Applied Mathematics, A.A.Samarskii, M.P.Sapagovas, eds., Elsevier, 1992, p.57-65.
10. S.V. Ershov, A.B. Potapov. Macrodynamics:  large-scale structures in turbulent media. XVIII Int.  Conf.  Theor.  Appl.  Mech Haifa, Aug.22-28, 1992. p.51
11. S.V.Ershov, G.G.Malinetskii, A.B.Potapov. Several types of dissipative structures and chaotic regimes in nonlinear media. In: All-Union Conference “Nonlinear Phenomena”, Moscow, 1989, p.15-16 (in Russian)
12. S.P. Kurdyumov, G.G. Malinetskii, A.B. Potapov. Resonant influence symmetry and spectrum of structures in nonlinear media. "Symmetry of structure", an interdisciplinary symposium, Budapest, 1989, p.297-300.
13. A.B. Potapov, G.G. Malinetskii. Symmetry and approximate study of multidimensional structures in nonlinear media. "Symmetry of structure", an interdisciplinary symposium, Budapest, 1989, p.439-441.
14. S.P. Kurdyumov, E.S. Kurkina, A.B. Potapov. Multidimensional nonstationary structures in the medium with nonlinear heat conduction coefficient and a source. All-Union Workshop “Mathematical and Computational Methods in Biology”, Puschino, 1985, 62-63.
 

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