Geodesic
Phenomenological computational models for passing outbreaks of insects with its bifurcation completion
Matematičeskoe modelirovanie, Tome 30 (2018) no. 1, pp. 40-54.

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The article discusses the model scenario of sharp increase in the number of insect phytophage, dangerous and poorly predictable phenomenon. The scenario based on possibility of increasing the efficiency of reproduction in the limited range of operation of the population. Time-limited local outbreak begins after overcoming the threshold in the form of an equilibrium point. Insect generations decrease rate slows, due to attenuation the customary mechanisms of death regulation that depends on the density of the pests. In the developed redefined computing take into account the structure of various vulnerable life stages before entry into fertile age, which is established for the European corn borer. Reducing the role of mortality factors it is unevenly distributed in the ontogenetic stages of the insect. Sharp inclusion mechanism of regulation of the exhaustion of resources, which is heavily because of the indirect competition between adult and larval stages, implemented by special supplement on the right side in the equation of generation mortality dynamics. We have described a variable effect of mortality regulation leads to a tangent bifurcation, which completes the phase of uncontrolled reproduction. In conclusion, we consider the corresponding dynamical system derived characteristics example of a real situation spontaneously decaying pest outbreaks.
Keywords: population models, scenario of insect outbreak, override computing structures
Mots-clés : tangent bifurcation, corn borer. 
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A. Yu. Perevaryukha. Phenomenological computational models for passing outbreaks of insects with its bifurcation completion. Matematičeskoe modelirovanie, Tome 30 (2018) no. 1, pp. 40-54. http://geodesic.mathdoc.fr/item/MM_2018_30_1_a3/

[1] Gauze G. F., Vitt A. A., “O periodicheskikh kolebaniiakh chislennosti populiatsii: matematicheskaia teoriia relaksatsionnogo vzaimodeistviia mezhdu khishchnikami i zhertvami i ee primenenie k populiatsiiam dvukh prosteishikh”, Izvestiia Akademii nauk SSSR. VII seriia. Otdelenie matematicheskikh i estestvennykh nauk, 1934, no. 10, 1551–1559 | Zbl

[2] Tittensor D. P., “Global patterns and predictors of marine biodiversity across taxa”, Nature, 466:7310 (2011), 1098–1101 | DOI

[3] Sharkovskii A. N., Romanenko E. Iu., “Raznostnye uravneniia i dinamicheskie sistemy, porozhdaemye nekotorymi klassami kraevykh zadach”, Tr. MIAN, 244, 2004, 281–296 | Zbl

[4] Kozhukhova V. N., “Sravnitelnyi analiz svoistv izvestnykh modelei logisticheskoi dinamiki”, Izvestiia Akademii upravleniia, 2011, no. 4, 46–52

[5] Barbosa P., Letourneau D., Agrawal A., Insect outbreaks revisited, John Wiley Sons, Oxford, 2012, 492 pp.

[6] De Melo W., van Strien S., “One-dimensional dynamics: The Schwarzian derivative and beyond”, Bulletin of the American Mathematical Society, 18:2 (1988), 159–162 | DOI | MR | Zbl

[7] Aulbach B., Kieninger B., “On Three Definitions of Chaos”, Nonlinear Dynamics and Systems Theory, 2001, no. 1, 23–37 | MR | Zbl

[8] Frolov A. N., “Bioticheskie faktory depressii kukuruznogo motylka”, Vestnik zashchity rastenii, 2004, no. 1, 37–47

[9] Kriksunov E. A., Snetkov M. A., “Model formirovaniia popolneniia nerestovogo stada s uchetom vesovogo rosta ryb”, Doklady AN SSSR, 253:3 (1980), 759–761

[10] Kolesov Y., Senichenkov Y., “Simulation of Variable Structure Models using Rand Model Designer”, Proceedings of the 2013 8th EUROSIM Congress on Modelling and Simulation, 294–299

[11] Gilpin M. E., Soule M. E., “Minimum viable populations: The processes of species extinctions”, Conser-vation biology: The science of scarcity and diversity, Sinauer Associates, Sunderland, 1986, 13–34

[12] Keitt T. H., Lewis M. A., Holt R. D., “Allee effects, invasion pinning, and species borders”, The American Naturalist, 157:2 (2001), 203–216

[13] Tobin P. C., “The role of Allee effects in gypsy moth, Lymantria dispar (L.), invasions”, Population Ecolog, 51 (2009), 373–384 | DOI

[14] Senichenkov Iu. B., Kolesov Iu. B., Inikhov D. B., “Formy predstavleniia dinamicheskikh sistem v MvStudium”, Kompiuternye instrumenty v obrazovanii, 2007, no. 4, 44–49

[15] Perevaryukha A. Y., “Uncertainty of asymptotic dynamics in bioresource management simulation”, Journal of Computer and Systems Sciences International, 50:3 (2011), 491–498 | DOI | MR | Zbl

[16] Feigenbaum M. J., “The transition to aperiodic behavior in turbulent systems”, Communications in Mathematical Physics, 77:1 (1980), 65–86 | DOI | MR | Zbl

[17] Graczyk J., Sands D., Swiatek G., “Metric attractors for smooth unimodal maps”, Annals of Mathematics, 159 (2004), 725–740 | DOI | MR | Zbl

[18] Astafev G. B., Koronovski A. A., Hramov A. E., “Behavior of dynamical systems in the regime of transient chaos”, Technical Physics Letters, 29:11 (2003), 923–926 | DOI

[19] Dushoff J., Huang W., Castillo-Chavez C., “Backwards bifurcations and catastrophe in simple models of fatal diseases”, Journal of Mathematical Biology, 36 (1998), 227–248 | DOI | MR | Zbl

[20] Clark L. R., “The population dynamics of Cardiaspina albitextura (Psyllidae)”, Australian Journal of Zoology, 12:3 (1964), 362–380 | DOI

[21] Palnikova E. N., Meteleva M. K., Sukhovolskii V. G., “Vliianie modifitsiruiushchikh faktorov na dinamiku chislennosti lesnykh nasekomykh i razvitie vspyshek massovogo razmnozheniia”, Lesovedenie, 2006, no. 5, 29–35