On existence of homoclinic orbits for some types of autonomous quadratic systems of differential equations

DOI10.1016/j.amc.2010.11.010zbMath1214.37016OpenAlexW1964959594MaRDI QIDQ621005

Vasiliy Ye. Belozyorov

Publication date: 2 February 2011

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2010.11.010

zbMATH Keywords

boundednesslinear transformationhomoclinic orbitchaotic attractorsystem of ordinary quadratic differential equationsnegative definiteness

Mathematics Subject Classification ID

Homoclinic and heteroclinic orbits for dynamical systems (37C29)

Related Items (11)

Bifurcation analysis and chaos control in Shimizu-Morioka chaotic system with delayed feedback ⋮ Homoclinic orbits for a class of second order dynamic equations on time scales via variational methods ⋮ Role of logistic and Ricker's maps in appearance of chaos in autonomous quadratic dynamical systems ⋮ Research of chaotic dynamics of 3D autonomous quadratic systems by their reduction to special 2D quadratic systems ⋮ Comment on `Šilnikov-type orbits of Lorenz-family systems' ⋮ Existence of heteroclinic and homoclinic orbits in two different chaotic dynamical systems ⋮ New types of 3-D systems of quadratic differential equations with chaotic dynamics based on Ricker discrete population model ⋮ Implicit one-dimensional discrete maps and their connection with existence problem of chaotic dynamics in 3-D systems of differential equations ⋮ Reduction Method for Search of Chaotic Attractors in Generic Autonomous Quadratic Dynamical Systems ⋮ Invariant Approach to Existence Problem of Chaos in 3D Autonomous Quadratic Dynamical Systems ⋮ GENERATING CHAOS IN 3D SYSTEMS OF QUADRATIC DIFFERENTIAL EQUATIONS WITH 1D EXPONENTIAL MAPS

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