GENERATING CHAOS IN 3D SYSTEMS OF QUADRATIC DIFFERENTIAL EQUATIONS WITH 1D EXPONENTIAL MAPS

DOI10.1142/S0218127413501058zbMath1272.34054MaRDI QIDQ2849231

Vasiliy Ye. Belozyorov, S. V. Chernyshenko

Publication date: 17 September 2013

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

zbMATH Keywords

limit cyclehomoclinic orbitchaotic attractor1D discrete mapordinary autonomous differential equations system

Mathematics Subject Classification ID

Complex behavior and chaotic systems of ordinary differential equations (34C28) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (6)

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 ⋮ Reduction Method for Search of Chaotic Attractors in Generic Autonomous Quadratic Dynamical Systems ⋮ General Method of Construction of Implicit Discrete Maps Generating Chaos in 3D Quadratic Systems of Differential Equations ⋮ Invariant Approach to Existence Problem of Chaos in 3D Autonomous Quadratic Dynamical Systems ⋮ Exponential-Algebraic Maps and Chaos in 3D Autonomous Quadratic Systems

Cites Work

• 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
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• 3-scroll and 4-scroll chaotic attractors generated from a new 3-D quadratic autonomous system
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• Existence of heteroclinic orbits of the Shil'nikov type in a 3D quadratic autonomous chaotic system
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• Constructing a new chaotic system based on the Šilnikov criterion
• The existence of homoclinic orbits to saddle-focus
• AN EXTENDED ŠIL'NIKOV HOMOCLINIC THEOREM AND ITS APPLICATIONS
• CLASSIFICATION OF CHAOS IN 3-D AUTONOMOUS QUADRATIC SYSTEMS-I: BASIC FRAMEWORK AND METHODS

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