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Conference publications

Abstracts

XXII conference

Bifurcation Study of the Ecological System

Gurina T.A.

Мoscow Aviation Institute (National Reseach University), Faculty "Applied Mathematics and Physics", Volokolamskoe shosse, 4, Moscow, 125993, Russia, Phone: (915)-281-23-87, E-mail: gurina-mai@mail.ru

1 pp. (accepted)

We consider models of ecological systems such as "prey-predator-superpredator" describes three systems of differential equations with several parameters (Volterra-Gause and Rosenzweig-MacArthur).

As bifurcation parameters are considered two parameters of the system, other parameters are fixed. For special points that are in the region of positive values of the variables, we construct a partition plane of two parameters on the field by the type of rough singular point of the linearized system. At the intersection of a pair of complex conjugate roots of the characteristic equation of the boundary of a saddle-focus with positive real part comes Andronov-Hopf bifurcation of birth of a stable limit cycle. Further explore the cascade of period doubling bifurcations cycle and subharmonic cascade Sharkovskii ending of a cycle period of three.

With a further change in the parameters appear in the system cycles homoclinic bifurcation cascade leading to the formation of a strange attractor. With transforms laid computing systems and evidence shows the existence of a homoclinic orbit of a saddle-focus, the destruction of which is the primary homoclinic bifurcation cascade and defined range of parameters in which it exists.

References

1. Магницкий Н.А., Сидоров С.В. Новые методы хаотической динамики. - М., Едиториал УРСС, 2004. 320 стр.

2. Гурина Т.А. Качественные методы дифференциальных уравнений в теории управления летательными аппаратами. – М., Издательство МАИ, 2014. 160 стр.



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