Phenomenological Computational Model for the Development of a Population Outbreak of Insects with Its Bifurcational Completion
Tóm tắt
The article discusses the model scenario of a sharp increase in the number of phytophagous insects, a dangerous and poorly predictable phenomenon. The scenario is based on the possibility of an increased reproduction efficiency of the state of the population in the range limited from above and from below. A time-limited local outbreak begins after overcoming the threshold equilibrium point. The slowdown in the rate of loss of generations is caused by the attenuation of the customary mechanisms of density regulation. The developed redefined computational structure takes into account the structure of various vulnerabilities of life stages before entry into the fertile age, which is established for the European corn borer. Reduction of the role of mortality factors will be unevenly distributed in the ontogenetic stages of the insect. The sudden start of the regulation mechanism due to the exhaustion of resources, which is strengthened because of the indirect competition between the adult and larval stages, is implemented by a special supplement on the right side in the equation of the population size decrease. The described variable effect of mortality regulation leads to a tangential bifurcation, which completes the phase of uncontrolled reproduction. In conclusion, we consider an example of a real situation of spontaneously decaying outbreaks of a pest vulnerable for its enemies corresponding to the derived characteristics of a dynamical system.
Tài liệu tham khảo
G. F. Gauze and A. A. Vitt, “On periodic fluctuations in population size: the mathematical theory of relaxation interaction between predators and victims and its application to populations of two protozoa,” Izv. Akad. Nauk SSSR, VII Ser., Otd. Mat. Estestv. Nauk, No. 10, 1551–1559 (1934).
D. P. Tittensor, “Global patterns and predictors of marine biodiversity across taxa,” Nature 466 (7310), 1098–1101 (2011).
A. N. Sharkovskii and E. Yu. Romanenko, “Difference equations and dynamical systems generated by certain classes of boundary value problems,” Proc. Steklov Inst. Math. 244, 264–279 (2004).
V. N. Kozhukhova, “Comparative analysis concerning features of the well-known logistic dynamics models,” Izv. Akad. Upravl., No. 4, 46–52 (2011).
P. Barbosa, D. Letourneau, and A. Agrawal, Insect Outbreaks Revisited (Wiley, Oxford, 2012).
W. de Melo and S. van Strien, “One-dimensional dynamics: the Schwarzian derivative and beyond,” Bull. Am. Math. Soc. 18, 159–162 (1988).
B. Aulbach and B. Kieninger, “On three definitions of chaos,” Nonlin. Dyn. Syst. Theory, No. 1, 23–37 (2001).
A. N. Frolov, “Biotic factors of corn moth depression,” Vestn. Zashch. Rasten., No. 1, 37–47 (2004).
E. A. Kriksunov and M. A. Snetkov, “Model of the formation of the replenishment of the spawning herd taking into account the weight growth of fish,” Dokl. AN SSSR 253, 759–761 (1980).
Y. Kolesov and Y. Senichenkov, “Simulation of variable structure models using rand model designer,” in Proceedings of the 2013 8th EUROSIM Congress on Modelling and Simulation, pp. 294–299.
M. E. Gilpin and M. E. Soule, “Minimum viable populations: the processes of species extinctions,” in Conservation Biology: The Science of Scarcity and Diversity (Sinauer Assoc., Sunderland, 1986), pp. 13–34.
T. H. Keitt, M. A. Lewis, and R. D. Holt, “Allee effects, invasion pinning, and species borders,” Am. Natural. 157, 203–216 (2001).
P. C. Tobin, “The role of Allee effects in gypsy moth, Lymantria dispar (L.), invasions,” Populat. Ecol. 51, 373–384 (2009).
Yu. B. Senichenkov, Yu. B. Kolesov, and D. B. Inikhov, “Representation forms of dynamic systems in MvStudium,” Kompyut. Instrum. Obrazov., No. 4, 44–49 (2007).
A. Y. Perevaryukha, “Uncertainty of asymptotic dynamics in bioresource management simulation,” J. Comput. Syst. Sci. Int. 50, 491–498 (2011).
M. J. Feigenbaum, “The transition to aperiodic behavior in turbulent systems,” Commun. Math. Phys. 77, 65–86 (1980).
J. Graczyk, D. Sands, and G. Swiatek, “Metric attractors for smooth unimodal maps,” Ann. Math. 159, 725–740 (2004).
G. B. Astafev, A. A. Koronovski, and A. E. Hramov, “Behavior of dynamical systems in the regime of transient chaos,” Tech. Phys. Lett. 29, 923–926 (2003).
J. Dushoff, W. Huang, and C. Castillo-Chavez, “Backwards bifurcations and catastrophe in simple models of fatal diseases,” J. Math. Biol. 36, 227–248 (1998).
L. R. Clark, “The population dynamics of Cardiaspina albitextura (Psyllidae),” Austral. J. Zool. 12, 362–380 (1964).
E. N. Palnikova, M. K. Meteleva, and V. G. Sukhovolskii, “The influence of modifying factors on the dynamics of forest insect numbers and development of their outbreaks,” Lesovedenie, No. 5, 29–35 (2006).