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Conference publicationsAbstractsXXII conferenceBifurcation Study of the Ecological SystemМoscow 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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