Publication List Structured to Subjects

Note that, due to the idea behind this list, the same paper or book can appear in more than one section!

Models of dynamics and monitoring of complex multiscale (agro)ecological systems

  • Petrovskaya, N., and Petrovskii, S.V. (2017) Catching ghosts with a coarse net: use and abuse of spatial sampling data in detecting synchronization. J. R. Soc. Interface 14, 20160855.
  • Forbes E., Back M., Brooks A., Petrovskaya N., Petrovskii, S.V., Pope T., and Walters KFA. (2017) Sustainable management of slugs in commercial fields: assessing the potential for targeting control measures. Aspects of Applied Biology 134, 89-96.
  • Alharbi, W.G., and Petrovskii, S.V. (2016). The impact of fragmented habitat’s size and shape on populations with Allee effect. Mathematical Modelling of Natural Phenomena 11(4), 5-15.
  • Bearup, D., Petrovskaya, N., and Petrovskii, S.V. (2015) Some analytical and numerical approaches to understanding trap counts resulting from pest insect immigration. Mathematical Biosciences 263, 143-160.
  • Petrovskii, S.V., Petrovskaya, N., and Bearup, D. (2014) Multiscale approach to pest insect monitoring: Random walks, pattern formation, synchronization, and networks. Physics of Life Reviews 11, 467-525.
  • Petrovskii, S.V., Petrovskaya, N., and Bearup, D. (2014) Multiscale ecology of agroecosystems is an emerging research field that can provide a stronger theoretical background for the integrated pest management. Physics of Life Reviews 11, 536-539.
  • Bearup, D., Petrovskii, S.V., Blackshaw, R., and Hastings, A. (2013) The impact of terrain and weather conditions on the metapopulation of Tipula paludosa in South-Western Scotland: linking pattern to process. American Naturalist 182, 393-409.
  • Lewis, M.A., Maini, P., and Petrovskii, S.V., Eds. (2013) Dispersal, Individual Movement, and Spatial Ecology: A Mathematical Perspective. Springer Lecture Notes in Mathematics, Vol.~2071. Springer.
  • Petrovskii, S.V., and Petrovskaya, N.B. (2012) Computational ecology as an emerging science. Interface Focus 2, 241-254.
  • Petrovskii, S.V., Bearup, D., Ahmed, D.A., Blackshaw, R. (2012) Estimating insect population density from trap counts. Ecol. Compl. 10, 69-82.
  • Petrovskaya, N.B., Petrovskii, S.V., and Murchie, A.K. (2012) Challenges of ecological monitoring: estimating population abundance from sparse trap counts. J. R. Soc. Interface 9, 420-435.
  • Hastings, A., Petrovskii, S., and Morozov, A. (2011) Spatial ecology across scales. Biol. Lett. 7, 163-165.
  • Petrovskaya, N.B., and Petrovskii, S.V. (2010) The coarse-grid problem in ecological monitoring. Proc.~R.~Soc.~A 466, 2933-2953.
  • Blackshaw, R., and Petrovskii, S.V. (2007). Limitation and regulation of ecological populations: a meta-analysis of Tipula paludosa field data. Mathematical Modelling of Natural Phenomena 2(4), 46-62.
  • Malchow, H., Petrovskii, S.V., and Medvinsky, A.B. (2002) Numerical study of plankton-fish dynamics in a spatially structured and noisy environment. Ecological Modelling 149, 247-255.
  • Petrovskii, S.V., and Li, B.-L. (2001) Increased coupling between sub-populations in a spatially structured environment can lead to population outbreaks. Journal of Theoretical Biology 212, 549-562.

 

Global environmental change

  • Petrovskii, S.V., Sekerci, Y., and Venturino, E. (2017) Regime shifts and ecological catastrophes in a model of plankton-oxygen dynamics under the climate change. J. Theor. Biol. 424, 91-109.
  • Sekerci, Y., and Petrovskii, S.V. (2015) Mathematical modelling of plankton-oxygen dynamics under the climate change. Bull. Math. Biol. 77, 2325-2353.

 

Mathematics of biological invasions

  • Petrovskaya, N., Petrovskii, S.V., and Zhang, W. (2017) Patchy, not patchy, or how much patchy? Classification of spatial patterns appearing in a model of biological invasion. Mathematical Modelling of Natural Phenomena, in press.
  • Lewis, M.A., Petrovskii, S.V., and Potts, J. (2016) The Mathematics Behind Biological Invasions. Interdisciplinary Applied Mathematics, Vol. 44. Springer, 362p.
  • Rodrigues, L.A.D., Mistro, D.C., Cara, E.R., Petrovskaya, N., and Petrovskii, S.V. (2015) Patchy invasion of stage-structured alien species with short-distance and long-distance dispersal. Bull. Math. Biol. 77, 1583-1619.
  • Jankovic, M., and Petrovskii, S.V. (2013) Gypsy moth invasion in North America: a simulation study of the spatial pattern and the rate of spread. Ecol. Compl. 14, 132-144.
  • Mistro, D.C., Rodrigues, L.A.D., and Petrovskii, S.V. (2012) Spatiotemporal complexity of biological invasion in a space- and time-discrete predator-prey system with the strong Allee effect. Ecological Complexity 9, 16-32.
  • Petrovskii, S.V., and McKay, K. (2010) Biological invasion and biological control: A case study of the gypsy moth spread. Aspects of Applied Biology 104, 37-48.
  • Morozov, A.Y., Petrovskii, S.V., and Li, B.-L. (2006) Spatiotemporal complexity of the patchy invasion in a predator-prey system with the Allee effect. Journal of Theoretical Biology 238, 18-35.
  • Petrovskii, S.V., and Li, B.-L. (2006) Exactly Solvable Models of Biological Invasion, Chapman & Hall / CRC Press, 217 p.
  • Petrovskii, S.V., Morozov, A.Y., and Li, B.-L. (2005) Regimes of biological invasion in a predator-prey system with the Allee effect. Bulletin of Mathematical Biology 67, 637-661.
  • Petrovskii, S.V., Malchow, H., Hilker, F.M., and Venturino, E. (2005) Patterns of patchy spread in deterministic and stochastic models of biological invasion and biological control. Biological Invasions 7, 771-793.
  • Morozov, A.Y., Nezlin, N.P., and Petrovskii, S.V. (2005) Invasion of a top predator into epipelagic ecosystem can bring a paradoxical top-down trophic control. Biological Invasions 7, 845-861.
  • Petrovskii, S.V., and Blackshaw, R. (2005) Gone with the wind: is it always true for invasive plants and, if not, why not? In Introduction and Spread of Invasive Species (D.V.Alford and G.F.Backhaus, eds.), p.277-278. BCPC Symposium Proceedings No. 81.
  • Petrovskii, S.V., and Li, B.-L. (2003). An exactly solvable model of population dynamics with density-dependent migrations and the Allee effect. Mathematical Biosciences 186, 79-91.
  • Petrovskii, S.V., Morozov, A.Y., and Venturino, E. (2002) Allee effect makes possible patchy invasion in a predator-prey system. Ecology Letters 5, 345-352.
  • Petrovskii, S.V., Kawasaki, K., Takasu, F., and Shigesada, N. (2001) Diffusive waves, dynamical stabilization and spatio-temporal chaos in a community of three competitive species. Japan Journal of Industrial and Applied Mathematics 18, 459-481.
  • Petrovskii, S.V., and Shigesada, N. (2001). Some exact solutions of a generalized Fisher equation related to the problem of biological invasion. Mathematical Biosciences 172, 73-94.
  • Petrovskii, S.V. (1999) Plankton front waves accelerated by marine turbulence. Journal of Marine Systems 21, 179-188.
  • Petrovskii, S.V. (1998) Modelling of open-sea ecological impact: impact wave localization and pattern formation.  Environment Modelling and Assessment 3, 127-133.
  • Barenblatt, G.I., Vinogradov, M.E., and Petrovskii, S.V. (1995) Impact waves in spatially inhomogeneous open-sea ecosystems: Localization and pattern formation. Oceanology 35, 202-207.
  • Barenblatt, G.I., Vinogradov, M.E., and Petrovskii, S.V. (1995) Formation and propagation of impact waves in ocean ecosystems. Engineering Ecology 1(3), 76-91.  [in Russian]
  • Vinogradov, M.E., Barenblatt, G.I., Gorbunov, A.E., and Petrovskii, S.V. (1993) Mathematical modeling of an ``impact'' in ecological systems. Transactions (Doklady) of Russian Academy of Science 328, 509-512.
  • Barenblatt, G.I., Vinogradov, M.E., Gorbunov, A.Y., and Petrovskii, S.V. (1993) Modeling impact waves in complex ecological systems. Oceanology 33, 1-7.

 

Models of individual animal movement

  • Tilles, P.F.C., Petrovskii, S.V., and Natti, P.L. (2017) A random acceleration model of individual animal movement allowing for diffusive, superdiffusive and superballistic regimes. Scientific Reports 7, 14364.
  • Choules, J.D., and Petrovskii, S.V. (2017) Which random walk is faster? Methods to compare different step length distributions in individual animal movement. Mathematical Modelling of Natural Phenomena 12(2), 22-45.
  • Tilles, P.F.C., Petrovskii, S.V., and Natti, P.L. (2016) A random walk description of individual animal movement accounting for periods of rest. R. Soc. Open Sci. 3, 160566.
  • Bearup, D., Benefer, C.M., Petrovskii, S.V., and Blackshaw, R. (2016) Revisiting Brownian motion as a description of animal movement: a comparison to experimental movement data. Methods in Ecology and Evolution 7, 1525-1537.
  • Tilles, P.F.C., and Petrovskii, S.V. (2016) How animals move along? Exactly solvable model of superdiffusive spread resulting from animal’s decision making. J. Math. Biol., 73, 227-255.
  • Tilles, P.F.C., and Petrovskii, S.V. (2015) Statistical mechanics of animal movement: animals's decision-making can result in superdiffusive spread. Ecol.~Compl. 22, 86-92.
  • Ahmed, D.A., and Petrovskii, S.V. (2015). Time dependent diffusion as a mean field counterpart of Levy type random walk. Mathematical Modelling of Natural Phenomena 10(2), 5-26.
  • Bearup, D., and Petrovskii, S.V. (2015) On time scale invariance of random walks in bounded space. J. Theor. Biol. 367, 230-245.
  • Kawai, R., and Petrovskii, S.V. (2012) Multi-scale properties of random walk models of animal movement: lessons from statistical inference. Proc. R. Soc. A 468, 1428-1451.
  • Petrovskii, S.V., Bearup, D., Ahmed, D.A., Blackshaw, R. (2012) Estimating insect population density from trap counts. Ecol. Compl. 10, 69-82.
  • Jansen, V.A.A., Mashanova, A., and Petrovskii, S.V. (2012) Model selection and animal movement: Comment on ``Levy walks evolve through interaction between movement and environmental complexity.'' Science 335, 918.
  • Petrovskii, S.V., Mashanova, A., and Jansen, V.A.A. (2011) Variation in individual walking behaviour creates the impression of a Levy flight. PNAS 108, 8704-8707.

 

Models of ecological pattern formation

  • Petrovskaya, N., Petrovskii, S.V., and Zhang, W. (2017) Patchy, not patchy, or how much patchy? Classification of spatial patterns appearing in a model of biological invasion. Mathematical Modelling of Natural Phenomena, in press.
  • Petrovskii, S.V. (2016) Pattern, process, scale, and model’s sensitivity. Physics of Life Reviews 19, 131-134.
  • Jankovic, M., Petrovskii, S.V., and Banerjee, M. (2016) Delay driven spatiotemporal chaos in single species population dynamics models. Theor. Popul. Biol. 110, 51-62.
  • Rodrigues, L.A.D., Mistro, D.C., and Petrovskii, S.V. (2011) Pattern formation in a space- and time-discrete predator-prey system with a strong Allee effect. Theor. Ecology 7, 77-88.
  • Rodrigues, L.A.D., Mistro, D.C., and Petrovskii, S. (2011) Pattern formation, long-term transients, and the Turing-Hopf bifurcation in a space-and time-discrete predator-prey system. Bull. Math. Biol. 73, 1812-1840.
  • Banerjee, M., and Petrovskii, S.V. (2011) Self-organised spatial patterns and chaos in a ratio-dependent predator-prey system. Theor.~Ecology 4,37-53.
  • Petrovskii, S.V., Morozov, A., Malchow, H., and M. Sieber, M. (2010) Noise can prevent onset of chaos in spatiotemporal population dynamics. Eur. Phys. J. B 78, 253-264.
  • Malchow, H., Petrovskii, S.V., and Venturino, E. (2008) Spatiotemporal Patterns in Ecology and Epidemiology: Theory, Models, Simulations. Chapman & Hall / CRC Press, 443 p.
  • Petrovskii, S.V., Malchow, H., Hilker, F.M., and Venturino, E. (2005) Patterns of patchy spread in deterministic and stochastic models of biological invasion and biological control. Biological Invasions 7, 771-793.
  • Petrovskii, S.V., Li, B.-L., and Malchow, H. (2004) Transition to spatiotemporal chaos can resolve the paradox of enrichment. Ecological Complexity 1, 37-47.
  • Morozov, A.Y., Petrovskii, S.V., and Li, B.-L. (2004). Bifurcations and chaos in a predator-prey system with the Allee effect. Proceedings of Royal Society of London B 271, 1407-1414.
  • Malchow, H., Hilker, F.M., and Petrovskii, S.V. (2004) Noise and productivity dependence of spatiotemporal pattern formation in a prey-predator system. Discrete and Continuous Dynamical Systems B 4, 707-713.
  • Malchow, H., Petrovskii, S.V., and M.Hilker, F. (2003) Models of spatiotemporal pattern formation in plankton dynamics.  Nova Acta Leopoldina 88, 325-340.
  • Petrovskii, S.V., Li, B.-L., and Malchow, H. (2003).  Quantification of the spatial aspect of chaotic dynamics in biological and chemical systems. Bulletin of Mathematical Biology 65, 425-446.
  • Malchow, H., Petrovskii, S.V., and M.Hilker, F. (2003) Models of spatiotemporal pattern formation in plankton dynamics.  Nova Acta Leopoldina 88, 325-340.
  • Petrovskii, S.V., Morozov, A.Y., and Venturino, E. (2002) Allee effect makes possible patchy invasion in a predator-prey system. Ecology Letters 5, 345-352.
  • Medvinsky, A.B., Petrovskii, S.V., Tikhonova, I.A., Tikhonov, D.A., Li, B.-L., Venturino, E., Malchow, H., and Ivanitskii, G.R. (2002) Spatio-temporal pattern formation, fractals and chaos in conceptual ecological models as applied to coupled plankton-fish dynamics. Physics-Uspekhi 45, 27-57.
  • Malchow, H., Petrovskii, S.V., and Medvinsky, A.B. (2002) Numerical study of plankton-fish dynamics in a spatially structured and noisy environment. Ecological Modelling 149, 247-255.
  • Malchow, H., and Petrovskii, S.V. (2002) Dynamical stabilization of an unstable equilibrium in chemical and biological systems. Mathematical and Computer Modelling 36, 307-319.
  • Medvinsky, A.B., Petrovskii, S.V., Tikhonova, I.A., Malchow, H., and Li, B.-L. (2002). Spatiotemporal complexity of plankton and fish dynamics. SIAM Review 44, 311-370.
  • Petrovskii, S.V., and Malchow, H. (2001).  Wave of chaos: new mechanism of pattern formation in spatio-temporal population dynamics, Theoretical Population Biology 59, 157-174.
  • Petrovskii, S.V., and Malchow, H. (2001) Spatio-temporal chaos in an ecological community as a response to unfavorable environmental changes. Advances in Complex Systems 4, 227-250.
  • Malchow, H., Petrovskii, S.V., and Medvinsky, A.B. (2001) Pattern formation in models of plankton dynamics. A synthesis. Oceanologica Acta 24, 479-487.
  • Petrovskii, S.V., and Malchow, H. (2000) Critical phenomena in plankton communities: KISS model revisited.  Nonlinear Analysis: Real World Applications 1, 37-51.
  • Malchow, H., Radtke, B., Kallache, M., Medvinsky, A.B., Tikhonov, D.A., and Petrovskii, S.V. (2000) Spatio-temporal pattern formation in coupled models of plankton dynamics and fish school motion. Nonlinear Analysis: Real World Applications 1, 53-67.
  • Petrovskii, S.V., and Malchow, H. (1999)  A minimal model of pattern formation in a prey-predator system.   Mathematical and Computer Modelling 29(8), 49-63.
  • Petrovskii, S.V., Vinogradov, M.E., and Malchow, H. (1999) On a possible mechanism of "patchiness" in the plankton spatial distribution. Transactions (Doklady) of Russian Academy of Science 367, 714-717.
  • Petrovskii, S.V. (1998) Modelling of open-sea ecological impact: impact wave localization and pattern formation.  Environment Modelling and Assessment 3, 127-133.

 

Conceptual models of plankton dynamics

  • Petrovskii, S.V., Sekerci, Y., and Venturino, E. (2017) Regime shifts and ecological catastrophes in a model of plankton-oxygen dynamics under the climate change. J. Theor. Biol. 424, 91-109.
  • Sekerci, Y., and Petrovskii, S.V. (2015) Mathematical modelling of plankton-oxygen dynamics under the climate change. Bull. Math. Biol. 77, 2325-2353.
  • Sekerci, Y., and Petrovskii, S.V. (2015). Mathematical modelling of spatiotemporal dynamics of oxygen in a plankton system. Mathematical Modelling of Natural Phenomena 10(2), 96-114.
  • Morozov, A., and Petrovskii, S.V. (2013) Feeding on multiple sources: towards a universal parameterization of the functional response of a generalist predator allowing for switching. PLoS One 8(9), e74586.
  • Korobeinokov, A., and Petrovskii, S.V. (2008) Toward a general theory of ecosystem stability: plankton-nutrient interaction as a paradigm. In Aspects of Mathematical Modelling. Applications in Science, Medicine, Economics and Management (E.Venturino and R.J.Hosking, eds.), p.~27-39.Basel: Birkhauser.
  • Malchow, H., Hilker, F.M., Siekmann, I., Petrovskii, S.V., and Medvinsky, A.B. (2008). Mathematical models of pattern formation in planktonic predation-diffusion systems. In Aspects of Mathematical Modelling. Applications in Science, Medicine, Economics and Management (E.Venturino and R.J.Hosking, eds.), p.~1–26. Basel: Birkhauser.
  • Morozov, A.Y., Petrovskii, S.V., and Nezlin, N.P. (2007) Towards resolving the paradox of enrichment: The impact of zooplankton vertical migrations on plankton systems stability. Journal of Theoretical Biology 248, 501-511.
  • Hilker, F.M., Malchow, H., Langlais, M., and Petrovskii, S.V. (2006) Oscillations and waves in a virally infected plankton system. Part II: Transition from lysogeny to lysis. Ecological Complexity 3, 200-208.
  • Sarkar, R.R., Petrovskii, S.V., Biswas, M., Gupta, A., and Chattopadhyay, J. (2006) An ecological study of a marine plankton community based on the field data collected from Bay of Bengal. Ecological Modelling 193, 589-601.
  • Petrovskii, S.V., and Malchow, H. (2005) Mathematical models of marine ecosystems. In The Encyclopedia of Life Support Systems (EOLSS), Developed under the Auspices of the UNESCO, EOLSS Publishers, Oxford UK [http://www.eolss.net].
  • Morozov, A.Y., Nezlin, N.P., and Petrovskii, S.V. (2005) Invasion of a top predator into epipelagic ecosystem can bring a paradoxical top-down trophic control. Biological Invasions 7, 845-861.
  • Malchow, H., Hilker, F.M., Petrovskii, S.V., and Brauer, K. (2004) Oscillations and waves in a virally infected plankton system, I. The lysogenic stage. Ecological Complexity 1, 211-223.
  • Malchow, H., Petrovskii, S.V., and M.Hilker, F. (2003) Models of spatiotemporal pattern formation in plankton dynamics.  Nova Acta Leopoldina 88, 325-340.
  • Malchow, H., Medvinsky, A.B., and Petrovskii, S.V. (2003) Patterns in models of plankton dynamics in a heterogeneous environment. In Handbook of Scaling Methods in Ecology: Measurement, Analysis, Simulation (L.Seurount and P.G.Strutton, eds.), p. 401-410. Paris: CRC Press.
  • Malchow, H., Petrovskii, S.V., and Medvinsky, A.B. (2002) Numerical study of plankton-fish dynamics in a spatially structured and noisy environment. Ecological Modelling 149, 247-255.
  • Medvinsky, A.B., Petrovskii, S.V., Tikhonova, I.A., Malchow, H., and Li, B.-L. (2002). Spatiotemporal complexity of plankton and fish dynamics. SIAM Review 44, 311-370.
  • Medvinsky, A.B., Tikhonova, I.A., Petrovskii, S.V., Malchow, H., and Venturino, E. (2002) Chaos and order in plankton dynamics: Complex behaviour of a simple model.  Zhurnal Obshchey Biologii 63(2), 149-158.
  • Medvinsky, A.B., Petrovskii, S.V., Tikhonova, I.A., Tikhonov, D.A., Li, B.-L., Venturino, E., Malchow, H., and Ivanitskii, G.R. (2002) Spatio-temporal pattern formation, fractals and chaos in conceptual ecological models as applied to coupled plankton-fish dynamics. Physics-Uspekhi 45, 27-57.
  • Malchow, H., Petrovskii, S.V., and Medvinsky, A.B. (2002) Numerical study of plankton-fish dynamics in a spatially structured and noisy environment. Ecological Modelling 149, 247-255.
  • Petrovskii, S.V., Vinogradov, M.E., and Morozov, A.Y. (2002) Spatio-temporal horizontal plankton patterns caused by biological invasion in a two-species model of plankton dynamics allowing for the Allee effect. Oceanology 42, 384- 393.
  • Medvinsky, A.B., Tikhonova, I.A., Petrovskii, S.V., Malchow, H., and Venturino, E. (2001) Chaos and order in spatially structured plankton dynamics. A theoretical study.  In Nonlinear Dynamics in the Life and Social Sciences (W.Sulis and I.Trofimova, eds.), p. 383-397. Amsterdam: IOS Press.
  • Medvinsky, A.B., Petrovskii, S.V., Tikhonov, D.A., Tikhonova, I.A., Ivanitsky, G.R., Venturino, E., and Malchow, H. (2001) Biological factors underlying regularity and chaos in aquatic ecosystems: simple models of complex dynamics.  Journal of Biophysics 26, 77-108.
  • Medvinsky, A.B., Petrovskii, S.V., Tikhonova, I.A., Venturino, E., and Malchow, H. (2001) Chaos and regular dynamics in model multi-habitat plankton-fish communities. Journal of Biophysics 26, 109-120.
  • Malchow, H., Petrovskii, S.V., and Medvinsky, A.B. (2001) Pattern formation in models of plankton dynamics. A synthesis. Oceanologica Acta 24, 479-487.
  • Petrovskii, S.V., and Malchow, H. (2000) Critical phenomena in plankton communities: KISS model revisited.  Nonlinear Analysis: Real World Applications 1, 37-51.
  • Malchow, H., Radtke, B., Kallache, M., Medvinsky, A.B., Tikhonov, D.A., and Petrovskii, S.V. (2000) Spatio-temporal pattern formation in coupled models of plankton dynamics and fish school motion. Nonlinear Analysis: Real World Applications 1, 53-67.
  • Morozov, A.Y., and Petrovskii, S.V. (2000) Mathematical modelling of the initial stage of a ``red tide'' accounting for the joint effect of various factors. Oceanology 40, 356-362.
  • Petrovskii, S.V. (1999) Plankton front waves accelerated by marine turbulence. Journal of Marine Systems 21, 179-188.
  • Petrovskii, S.V. (1999) On the diffusion of a plankton patch in a turbulent ocean. (1999) Oceanology 39, 737-742.
  • Petrovskii, S.V., Vinogradov, M.E., and Malchow, H. (1999) On a possible mechanism of ``patchiness'' in the plankton spatial distribution. Transactions (Doklady) of Russian Academy of Science 367, 714-717.
  • Petrovskii, S.V. (1995) On application of models of the predator-prey type for simulation of time course of open-sea communities. Oceanology 35, 86-91.
  • Barenblatt, G.I., Vinogradov, M.E., and Petrovskii, S.V. (1995) Impact waves in spatially inhomogeneous open-sea ecosystems: Localization and pattern formation. Oceanology 35, 202-207.

 

Dynamics of structured populations

  • Morozov, A.Y., Banerjee, M., and Petrovskii, S.V. (2016) Long-term transients and complex dynamics of a stage-structured population with time delay and the Allee effect. J. Theor. Biol. 396, 116-124.
  • Rodrigues, L.A.D., Mistro, D.C., Cara, E.R., Petrovskaya, N., and Petrovskii, S.V. (2015) Patchy invasion of stage-structured alien species with short-distance and long-distance dispersal. Bull. Math. Biol. 77, 1583-1619.
  • Rodrigues, L.A.D., Mistro, D.C., and Petrovskii, S.V. (2011) Pattern formation in a space- and time-discrete predator-prey system with a strong Allee effect. Theor. Ecology 7, 77-88.
  • Rodrigues, L.A.D., Mistro, D.C., and Petrovskii, S. (2011) Pattern formation, long-term transients, and the Turing-Hopf bifurcation in a space-and time-discrete predator-prey system. Bull.~Math.~Biol. 73, 1812-1840.
  • Petrovskii, S.V., and Morozov, A.Y. (2009) Dispersal in a statistically structured population: Fat tails revisited. American Naturalist 173, 278-289.
  • Lutscher, F., and Petrovskii, S.V. (2008) The importance of census times in discrete-time growth-dispersal models. Journal of Biological Dynamics 2, 55-63.
  • Petrovskii, S.V., Blackshaw, R.P., and Li, B.-L. (2008) Persistence of structured populations with and without the Allee effect under adverse environmental conditions. Bulletin of Mathematical Biology 70, 412-437.
  • Petrovskii, S.V., and Blackshaw, R. (2003).  Behaviourally structured populations persist longer under harsh environmental conditions. Ecology Letters 6, 455-462.

 

Waves, patterns and chaos in diffusion-reaction systems

  • Volpert, V., Petrovskii, S.V., and Zincenko A. (2017) Interaction of human migration and wealth distribution. Nonlinear Analysis 159, 408-423.
  • Potts, J.R., and Petrovskii, S.V. (2017) Fortune favours the brave: movement responses shape demographic dynamics in strongly competing populations. J. Theor. Biol. 420, 190-199.
  • Sieber, M., Malchow, H., and Petrovskii, S.V. (2010) Noise-induced suppression of periodic travelling waves in oscillatory reaction-diffusion systems. Proc. R. Soc. A 466, 1903-1917.
  • Volpert, V., and Petrovskii, S.V. (2009) Reaction-diffusion waves in biology. Physics of Life Reviews 6, 267–310.
  • Malchow, H., Petrovskii, S.V., and Venturino, E. (2008) Spatiotemporal Patterns in Ecology and Epidemiology: Theory, Models, Simulations, Chapman & Hall / CRC Press, 443 p.
  • Petrovskii, S.V., Malchow, H., and Li B.-L. (2005) An exact solution of a diffusive predator-prey system. Proceedings of Royal Society of London A 461, 1029-1053.
  • Morozov, A.Y., Petrovskii, S.V., and Li, B.-L. (2004). Bifurcations and chaos in a predator-prey system with the Allee effect. Proceedings of Royal Society of London B 271, 1407-1414.
  • Petrovskii, S.V., and Li, B.-L. (2003). An exactly solvable model of population dynamics with density-dependent migrations and the Allee effect. Mathematical Biosciences 186, 79-91.
  • Petrovskii, S.V. (1999) Exact solutions of the forced Burgers equation. Technical Physics 44, 181-187.
  • Petrovskii, S.V. (1997) Localization of a nonlinear switching wave in an active medium with an isolated inhomogeneity. Technical Physics 42, 866-871.
  • Petrovskii, S.V., Medvinsky, A.B., and Ivanitskii, G.R. (1997) On the effect of a dynamical ``confinement'' of a localized initial perturbation in a predator-prey- type system. Transactions (Doklady) of Russian Academy of Science 357, 550- 553.
  • Ognev, M.V., Petrovskii, S.V., and Prostokishin, V.M. (1995) Dynamics of formation of a switching wave in a dissipative bistable medium. Technical Physics 40, 521-524.
  • Petrovskii, S.V. (1994) Approximate determination of the magnitude of the critical size in the problem of the evolution of an impact. Journal of Engineering Physics and Thermophysics 66, 346-352.
  • Petrovskii, S.V. (1994) Stabilization of nonstationary switching waves in a dissipative medium with turbulent mixing. Technical Physics Letters 20(10), 778-780.
  • Petrovskii, S.V. (1994) Critical nucleation parameters in an active bistable medium. Technical Physics 39, 747-749.
  • Petrovskii, S.V. (1993) Effect of acceleration of a switching wave in a dissipative medium with a periodic inhomogeneity. Technical Physics Letters 19(7), 397-398.

 

Theoretical ecology, nonlinear dynamics

  • Potts, J.R., and Petrovskii, S.V. (2017) Fortune favours the brave: movement responses shape demographic dynamics in strongly competing populations. J. Theor. Biol. 420, 190-199.
  • Volpert, V., Petrovskii, S.V., and Zincenko A. (2017) Interaction of human migration and wealth distribution. Nonlinear Analysis 159, 408-423.
  • Zincenko, A., and Petrovskii, S.V. (2017) Dynamics of a two subpopulations system including immigration. Mathematical Modelling of Natural Phenomena 12(2), 46-57.
  • Jankovic, M., and Petrovskii, S.V. (2014) Are time delays always destabilizing? Revisiting the role of time delays and the Allee effect. Theor. Ecology 7, 335-349.
  • Morozov, A., and Petrovskii, S.V. (2013) Feeding on multiple sources: towards a universal parameterization of the functional response of a generalist predator allowing for switching. PLoS One 8(9), e74586.
  • Venturino, E., and Petrovskii, S.V. (2013) Spatiotemporal behaviour of a prey-predator system with a group defence for prey. Ecol. Compl. 14, 37-47.
  • Gorban, A., and Petrovskii, S. (2011) Collective dynamics: when one plus one does not make two. Mathematical Medicine and Biology 28(2), 85-88.
  • Morozov, A.Y., and Petrovskii, S.V. (2009) Excitable population dynamics, biological control failure, and spatiotemporal pattern formation in a model ecosystem. Bulletin of Mathematical Biology 71, 863-887.
  • Petrovskii, S.V., Morozov, A.Y., and Li, B.-L. (2008) On a possible origin of the fat-tailed dispersal in population dynamics. Ecological Complexity 5, 146-150.
  • Hilker, F.M., Langlais, M., Petrovskii, S.V., and Malchow, H. (2007) A diffusive SI model with Allee effect and application to FIV. Mathematical Biosciences 206, 61-80.
  • Petrovskaya, N.B., Petrovskii, S.V., and Li, B.-L. (2006) Biodiversity measures revisited. Ecological Complexity 3, 13-22.
  • Petrovskii, S.V., Vinogradov, M.E., and Morozov, A.Y. (1998) Spatio-temporal dynamics of a localized population burst in a community of a prey-predator type. Oceanology 38, 796-804.

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