PARAMETER CHARACTERISTICS FOR STABLE AND UNSTABLE SOLUTIONS IN NONLINEAR DISCRETE DYNAMICAL SYSTEMS

DOI10.1142/S0218127410027611zbMath1204.37022OpenAlexW2126704124MaRDI QIDQ3069923

Yu Guo, Albert C. J. Luo

Publication date: 2 February 2011

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

Full work available at URL: https://doi.org/10.1142/s0218127410027611

zbMATH Keywords

chaosbifurcationnonlinear discrete systemsHenon mapnegative mappingspositive mappings

Mathematics Subject Classification ID

Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Stability theory for smooth dynamical systems (37C75) Dynamical systems involving smooth mappings and diffeomorphisms (37C05)

Related Items (3)

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 ⋮ Implicit one-dimensional discrete maps and their connection with existence problem of chaotic dynamics in 3-D systems of differential equations

Cites Work

• Chaotic behavior in the Henon mapping
• On the Henon transformation
• Bifurcations of three-dimensional diffeomorphisms with non-simple quadratic homoclinic tangencies and generalized Hénon maps
• Rigorous numerical models for the dynamics of complex Hénon mappings on their chain recurrent sets
• Compound windows of the Hénon-map
• Chaotic dynamics of three-dimensional Hénon maps that originate from a homoclinic bifurcation
• Period doubling bifurcations for families of maps on \(R^ n\)
• A two-dimensional mapping with a strange attractor
• Period doubling and multifractals in 1-D iterative maps
• Quantitative universality for a class of nonlinear transformations
• The mapping dynamics of periodic motions for a three-piecewise linear system under a periodic excitation
• Simple mathematical models with very complicated dynamics

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