Exponential-Algebraic Maps and Chaos in 3D Autonomous Quadratic Systems

DOI10.1142/S0218127415500480zbMath1314.34091MaRDI QIDQ5259035

Vasiliy Ye. Belozyorov

Publication date: 24 June 2015

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

zbMATH Keywords

limit cyclehomoclinic and heteroclinic orbitssaddle-focus3D ordinary autonomous quadratic differential equations systemthe Lorenz system1D and 2D discrete exponential-algebraic mapsthe Lanford system

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Nonlinear ordinary differential equations and systems (34A34) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Complex behavior and chaotic systems of ordinary differential equations (34C28) Dynamical systems involving maps of the interval (37E05) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (14)

Admissible Perturbations of a Generalized Langford System ⋮ Role of logistic and Ricker's maps in appearance of chaos in autonomous quadratic dynamical systems ⋮ Complex dynamics in a generalized Langford system ⋮ On novel conditions of chaotic attractors existence in autonomous polynomial dynamical systems ⋮ A novel search method of chaotic autonomous quadratic dynamical systems without equilibrium points ⋮ Remote state estimation problem: towards the data-rate limit along the avenue of the second Lyapunov method ⋮ Chaos in essentially singular 3D dynamical systems with two quadratic nonlinearities ⋮ Langford model: dynamics, bifurcations, attractors ⋮ New Heteroclinic Orbits Coined ⋮ Perturbations of the Lanford System Which Do Not Change the Reflecting Function ⋮ Completely integrable dynamical systems of Hopf-Langford type ⋮ 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 ⋮ Universal approach to the problem of emergence of chaos in autonomous dynamical systems

Cites Work

• Unnamed Item
• New types of 3-D systems of quadratic differential equations with chaotic dynamics based on Ricker discrete population model
• Critical homoclinic orbits lead to snap-back repellers
• Elements of applied bifurcation theory.
• Bifurcations and chaotic behavior on the Lanford system
• Bounded quadratic systems in the plane
• GENERATING CHAOS IN 3D SYSTEMS OF QUADRATIC DIFFERENTIAL EQUATIONS WITH 1D EXPONENTIAL MAPS
• RECENT DEVELOPMENTS IN DYNAMICAL SYSTEMS: THREE PERSPECTIVES
• CONSTRUCTING CHAOTIC POLYNOMIAL MAPS
• CLASSIFICATION OF CHAOS IN 3-D AUTONOMOUS QUADRATIC SYSTEMS-I: BASIC FRAMEWORK AND METHODS
• PHASE CHAOS IN THE DISCRETE KURAMOTO MODEL
• CHAOS ON ONE-DIMENSIONAL COMPACT METRIC SPACES
• TWO-DIMENSIONAL DYNAMICAL SYSTEMS WITH PERIODIC COEFFICIENTS
• General Method of Construction of Implicit Discrete Maps Generating Chaos in 3D Quadratic Systems of Differential Equations
• BIFURCATION DYNAMICS OF THREE-DIMENSIONAL SYSTEMS
• GENERATING MULTISCROLL CHAOTIC ATTRACTORS: THEORIES, METHODS AND APPLICATIONS
• A mathematical example displaying features of turbulence

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