Oscillations and waves in a virally infected plankton system

Abramson, 2003, Traveling waves of infection in the Hantavirus epidemics, Bull. Math. Biol., 65, 519, 10.1016/S0092-8240(03)00013-2 Allen, L., 2003. An Introduction to Stochastic Processes with Applications to Biology. Pearson Education, Upper Saddle River, NJ. Anishenko, V., Astakov, V., Neiman, A., Vadivasova, T., Schimansky-Geier, L., 2003. Nonlinear dynamics of chaotic and stochastic systems. Tutorial and modern developments. Springer Series in Synergetics. Springer, Berlin. Beltrami, 1994, Modelling the role of viral disease in recurrent phytoplankton blooms, J. Math. Biol., 32, 857, 10.1007/BF00168802 Chattopadhyay, 2002, Viral infection on phytoplankton-zooplankton system—a mathematical model, Ecol. Model., 151, 15, 10.1016/S0304-3800(01)00415-X Chattopadhyay, 2003, Dynamics of nutrient-phytoplankton interaction in the presence of viral infection, BioSystems, 68, 5, 10.1016/S0303-2647(02)00055-2 Dietz, 1985, Proportionate mixing models for age-dependent infection transmission, J. Math. Biol., 22, 117, 10.1007/BF00276550 Fuhrman, 1999, Marine viruses and their biogeochemical and ecological effects, Nature, 399, 541, 10.1038/21119 Grenfell, 2001, Travelling waves and spatial hierarchies in measles epidemics, Nature, 414, 716, 10.1038/414716a Higham, 2001, An algorithmic introduction to numerical simulation of stochastic differential equations, SIAM Rev., 43, 525, 10.1137/S0036144500378302 Jacquet, 2002, Flow cytometric analysis of an Emiliana huxleyi bloom terminated by viral infection, Aquat. Microb. Ecol., 27, 111, 10.3354/ame027111 Jiang, 1998, Significance of lysogeny in the marine environment: studies with isolates and a model of lysogenic phage production, Microb. Ecol., 35, 235, 10.1007/s002489900079 Kloeden, P., Platen, E., 1992. Numerical Solution of Stochastic Differential Equations. In: Applications of Mathematics, vol. 23. Springer, Berlin. Kuznetsov, 1992, Bifurcations and chaos in a periodic predator-prey model, Int. J. Bifurcat. Chaos, 2, 117, 10.1142/S0218127492000112 Lin, 2003, Traveling waves in a model of influenza A drift, J. Theor. Biol., 222, 437, 10.1016/S0022-5193(03)00056-0 Malchow, 1993, Spatio-temporal pattern formation in nonlinear nonequilibrium plankton dynamics, Proc. R. Soc. Lond. B, 251, 103, 10.1098/rspb.1993.0015 Malchow, 1996, Nonlinear plankton dynamics and pattern formation in an ecohydrodynamic model system, J. Mar. Sys., 7, 193, 10.1016/0924-7963(95)00012-7 Malchow, 2000, Motional instabilities in predator-prey systems, J. Theor. Biol., 204, 639, 10.1006/jtbi.2000.2074 Malchow, 2000, Nonequilibrium spatio-temporal patterns in models of nonlinear plankton dynamics, Freshwater Biol., 45, 239, 10.1046/j.1365-2427.2000.00550.x Malchow, 2004, Noise and productivity dependence of spatiotemporal pattern formation in a prey-predator system, Discrete Continuous Dynamical Sys. B, 4, 707 Malchow, H., Medvinsky, A., Petrovskii, S., 2004b. Patterns in models of plankton dynamics in a heterogeneous environment. In: Seuront, L., Strutton, P. (Eds.), Handbook of Scaling Methods in Aquatic Ecology: Measurement, Analysis, Simulation. CRC Press, Boca Raton, pp. 401–410. Malchow, 2002, Numerical study of plankton-fish dynamics in a spatially structured and noisy environment, Ecol. Model., 149, 247, 10.1016/S0304-3800(01)00467-7 Malchow, 2002, Dynamical stabilization of an unstable equilibrium in chemical and biological systems, Math. Comput. Model., 36, 307, 10.1016/S0895-7177(02)00127-9 Malchow, 2003, Models of spatiotemporal pattern formation in plankton dynamics, Nova Acta Leopoldina, NF, 88, 325 Malchow, 2001, Pattern formation in models of plankton dynamics. A synthesis, Oceanol. Acta, 24, 479, 10.1016/S0399-1784(01)01161-6 McCallum, 2001, How should pathogen transmission be modelled?, TREE, 16, 295 McDaniel, 2002, Lysogeny in Synechococcus, Nature, 415, 496, 10.1038/415496a Medvinsky, 2002, Spatiotemporal complexity of plankton and fish dynamics, SIAM Rev., 44, 311, 10.1137/S0036144502404442 Medvinsky, 2000, Fish and plankton interplay determines both plankton spatio-temporal pattern formation and fish school walks. A theoretical study, Nonlinear Dynamics, Psychol. Life Sci., 4, 135, 10.1023/A:1009580311610 Menzinger, M., Rovinsky, A., 1995. The differential flow instabilities. In: Kapral, R., Showalter, K. (Eds.), Chemical Waves and Patterns. Understanding Chemical Reactivity, vol. 10. Kluwer Academic Publishers, Dordrecht, pp. 365–397. Nold, 1980, Heterogeneity in disease-transmission modeling, Math. Biosci., 52, 227, 10.1016/0025-5564(80)90069-3 Ortmann, 2002, Lysogeny and lytic viral production during a bloom of the cyanobacterium Synechococcus spp, Microb. Ecol., 43, 225, 10.1007/s00248-001-1058-9 Pascual, 1993, Diffusion-induced chaos in a spatial predator-prey system, Proc. R. Soc. Lond. B, 251, 1, 10.1098/rspb.1993.0001 Petrovskii, 1999, A minimal model of pattern formation in a prey-predator system, Math. Comput. Model., 29, 49, 10.1016/S0895-7177(99)00070-9 Petrovskii, 2000, Critical phenomena in plankton communities: KISS model revisited, Nonlinear Anal. Real World Appl., 1, 37, 10.1016/S0362-546X(99)00392-2 Petrovskii, 2001, Wave of chaos: new mechanism of pattern formation in spatio-temporal population dynamics, Theor. Popul. Biol., 59, 157, 10.1006/tpbi.2000.1509 Rinaldi, 1993, Multiple attractors, catastrophes and chaos in seasonally perturbed predator-prey communities, Bull. Math. Biol., 55, 15, 10.1007/BF02460293 Sarkar, 2003, Occurence of planktonic blooms under environmental fluctuations and its possible control mechanism—mathematical models and experimental observations, J. Theor. Biol., 224, 501, 10.1016/S0022-5193(03)00200-5 Satnoianu, 2000, Non-Turing stationary patterns in flow-distributed oscillators with general diffusion and flow rates, Phys. Rev. E, 62, 113, 10.1103/PhysRevE.62.113 Satnoianu, 2000, Turing instabilities in general systems, J. Math. Biol., 41, 493, 10.1007/s002850000056 Scheffer, 1991, Fish and nutrients interplay determines algal biomass: a minimal model, OIKOS, 62, 271, 10.2307/3545491 Scheffer, 1991, Should we expect strange attractors behind plankton dynamics—and if so, should we bother?, J. Plankton Res., 13, 1291, 10.1093/plankt/13.6.1291 Scheffer, 1997, Seasonal dynamics of daphnia and algae explained as a, periodically forced predator-prey system, OIKOS, 80, 519, 10.2307/3546625 Sherratt, 1995, Ecological chaos in the wake of invasion, Proc. Natl. Acad. Sci. USA, 92, 2524, 10.1073/pnas.92.7.2524 Steele, 1992, A simple model for plankton patchiness, J. Plankton Res., 14, 1397, 10.1093/plankt/14.10.1397 Steffen, 1997, Effects of seasonal perturbation on a model plankton community, Environ. Model. Assess., 2, 43, 10.1023/A:1019096924487 Suttle, C., 2000. Ecological, evolutionary, and geochemical consequences of viral infection of cyanobacteria and eukaryotic algae. In: Hurst, C. (Ed.), Viral Ecology. Academic Press, San Diego, pp. 247–296. Suttle, 1990, Infection of phytoplankton by viruses and reduction of primary productivity, Nature, 347, 467, 10.1038/347467a0 Thomas, J., 1995. Numerical partial differential equations: finite difference methods. In: Texts in Applied Mathematics, vol. 22. Springer, New York. Truscott, 1994, Ocean plankton populations as excitable media, Bull. Math. Biol., 56, 981, 10.1007/BF02458277 Wilcox, 1994, Bacterial viruses in coastal sea, water: lytic rather than lysogenic production, Max. Ecol. Prog. Ser., 114, 35, 10.3354/meps114035 Wommack, 2000, Virioplankton: viruses in aquatic ecosystems, Microb. Molec. Biol. Rev., 64, 69, 10.1128/MMBR.64.1.69-114.2000 Zhdanov, 2003, Propagation of infection and the prey-predator interplay, J. Theor. Biol., 225, 489, 10.1016/S0022-5193(03)00291-1