6533b862fe1ef96bd12c62f4
RESEARCH PRODUCT
Digit replacement: A generic map for nonlinear dynamical systems
Vladimir García-moralessubject
Surface (mathematics)Computer scienceApplied MathematicsGeneral Physics and AstronomyFOS: Physical sciencesStatistical and Nonlinear PhysicsParameter spaceNonlinear Sciences - Chaotic Dynamics01 natural sciences010305 fluids & plasmasNonlinear systemSimple (abstract algebra)Aperiodic graphPhase space0103 physical sciencesAttractorOrbit (dynamics)Statistical physicsChaotic Dynamics (nlin.CD)010306 general physicsMathematical Physicsdescription
A simple discontinuous map is proposed as a generic model for nonlinear dynamical systems. The orbit of the map admits exact solutions for wide regions in parameter space and the method employed (digit manipulation) allows the mathematical design of useful signals, such as regular or aperiodic oscillations with specific waveforms, the construction of complex attractors with nontrivial properties as well as the coexistence of different basins of attraction in phase space with different qualitative properties. A detailed analysis of the dynamical behavior of the map suggests how the latter can be used in the modeling of complex nonlinear dynamics including, e.g., aperiodic nonchaotic attractors and the hierarchical deposition of grains of different sizes on a surface.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2016-10-27 |