TY - JOUR

T1 - Visualization of Four Normal Size Limit Cycles in Two-Dimensional Polynomial Quadratic System

AU - Kuznetsov, N. V.

AU - Kuznetsova, O. A.

AU - Leonov, G. A.

N1 - Funding Information: Acknowledgments This work was partly supported by Grants programm of the President of RF, Ministry of Education and Science of RF, Academy of Finland, RFBR and Saint-Petersburg State University.

PY - 2013/1

Y1 - 2013/1

N2 - This paper is devoted to analytical and numerical investigation of limit cycles in two-dimensional polynomial quadratic systems. The appearance of modern computers permits one to use a numerical simulation of complicated nonlinear dynamical systems and to obtain new information on a structure of their trajectories. However the possibilities of naive approach, based on the construction of trajectories by numerical integration of the considered differential equations, turns out to be very limited. In the paper the effective analytical-numerical methods for investigation of limit cycles in two-dimensional polynomial quadratic system are discussed. Estimations of domains of parameters, corresponding to existence of different configurations of large limit cycles, are obtained and visualization of four large limit cycles in quadratic system is presented.

AB - This paper is devoted to analytical and numerical investigation of limit cycles in two-dimensional polynomial quadratic systems. The appearance of modern computers permits one to use a numerical simulation of complicated nonlinear dynamical systems and to obtain new information on a structure of their trajectories. However the possibilities of naive approach, based on the construction of trajectories by numerical integration of the considered differential equations, turns out to be very limited. In the paper the effective analytical-numerical methods for investigation of limit cycles in two-dimensional polynomial quadratic system are discussed. Estimations of domains of parameters, corresponding to existence of different configurations of large limit cycles, are obtained and visualization of four large limit cycles in quadratic system is presented.

KW - 16th Hilbert problem

KW - Limit cycle

KW - Quadratic system

KW - Visualization

UR - http://www.scopus.com/inward/record.url?scp=84864289367&partnerID=8YFLogxK

U2 - 10.1007/s12591-012-0118-6

DO - 10.1007/s12591-012-0118-6

M3 - Article

VL - 21

SP - 29

EP - 34

JO - Differential Equations and Dynamical Systems

JF - Differential Equations and Dynamical Systems

SN - 0971-3514

IS - 1-2

ER -