BOUNDARY CRISIS OF ATTRACTOR IN THE SIMULATION CAUSES OF THE DEGRADATION OF COMMERCIAL BIORESOURCES
Abstract
The article describes the computational model that unites the formalization of ecological features of the reproductive cycle of anadromous fish and the possibility of studying nonlinear effects in the population dynamics under anthropogenic impact. Event-driven component implemented in continuous time has allowed us to take into account changes in the survival generation in interrelation with the factors of growth rate. Discrete component trajectory of the dynamical system has two areas of attraction and is characterized by the reverse tangent bifurcation due to the impact of fishing, which dramatically transforms the population with the condition of irregular fluctuations in low numbers. The further emergence of «boundary crisis» for the interval attractor describes a common scenario an irreversible degradation of biological resources.
About the Author
A. Yu. PerevarukhaRussian Federation
References
1. Feigenbaum M. J. Universal behavior in nonlinear systems / M. J. Feigenbaum // Physica D.– 1983.– Vol. 7, № 1–3.– P. 16–39.
2. Perevaryukha A. Yu. Cyclic and unstable chaotic dynamics in models of two populations of sturgeon fish / A. Yu Perevaryukha. // Numerical Analysis and Applications.– 2012.– Vol. 5, № 3.– Р. 254–264.
3. Singer D. Stable orbits and bifurcations of the maps on the interval / D. Singer // SIAM journal of applied math.– 1978.– V. 35.– P. 260–268.
4. Vellekoop М. On intervals, transitivity = chaos / М. Vellekoop, R. Berglund // The American Mathematical Monthly.– 1994.– Vol. 101, № 4.– P. 353–355.
5. Ricker W. E. Stock and recruitment / W. E. Ricker // Journal Fisheries research board of Canada.– 1954.– Vol. 11, № 5.– P. 559–623.
6. Paar V. Sensitive dependence of lifetimes of chaotic transient on numerical accuracy for a model with dry friction and frequency dependent driving amplitude / V. Paar, N. Pavin // Modern Physics Letters B.– 1996.– Vol. 10, № 4.– P.153–159.
7. Grebogi C. Chaotic attractors in crisis / C. Grebogi, E. Ott, J. A. Yorke // Physical Review Letters.– 1982.– Vol. 48, № 22.– P. 1507–1510.
8. Grebogi C. Chaos, strange attractors and fractal basin boundaries in nonlinear dynamics / C. Grebogi, E. Ott, J. A. Yorke // Science.– 1987.– Vol. 238, № 4827.– P. 632–638.
9. Minto C. Survival variability and population density in fish populations / C. Minto, R. A. Myers, W. Blanchard // Nature.– 2008.– Vol. 452.– P. 344–348.
Review
For citations:
Perevarukha A.Yu. BOUNDARY CRISIS OF ATTRACTOR IN THE SIMULATION CAUSES OF THE DEGRADATION OF COMMERCIAL BIORESOURCES. «System analysis and applied information science». 2015;(3):4-8. (In Russ.)