Symbolic Dynamics Generated by a Hybrid Chaotic Systems
Carlos Correia Ramos, Ana Isabel Santos, Sandra Vinagre
Journal of Advances in Mathematics and Computer Science · pp. 1–12 · Published 12 Aug 2016
10.9734/BJMCS/2016/27863Abstract
We consider piecewise defined differential dynamical systems which can be analysed through symbolic dynamics and transition matrices. We have a continuous regime, where the time flow is characterized by an ordinary differential equation (ODE) which has explicit solutions, and the singular regime, where the time flow is characterized by an appropriate transformation. The symbolic codification is given through the association of a symbol for each distinct regular system and singular system. The transition matrices are then determined as linear approximations to the symbolic dynamics. We analyse the dependence on initial conditions, parameter variation and the occurrence of global strange attractors.
References (5)
- 1 A periodically forced piecewise linear oscillator [DOI]
- 2 On iterated maps of the interval [DOI]
- 3 Sensitive dependence to initial conditions for one dimensional maps [DOI]
- 4 Periodic motions and grazing in a harmonically forced, piecewise, linear oscillator with impacts [DOI]
- 5 Invariants for the topological characterization of the iteration of differentiable functions – the bimodal case [DOI]
Cited by 2
Carlos Ramos, Ana Isabel Santos, Sandra Vinagre · Springer Proceedings in Mathematics & Statistics · 2020
Showing 1 of 2 known citations — external sources report more than can currently be individually listed.
Related research
- Chaos and Boundary Values Problems of Mathematical Models of Nonautonomous Dynamical Systems — shares topic coverage
- Variation Mass Effects on the Stability of Libration Points of Restricted Three Body Problem (Laplace Transformation) — shares topic coverage
- Traveling Wave Solutions for a Coupled KdV Equations — shares topic coverage
- Existence of Random Attractors for a Stochastic Strongly Damped Plate Equations with Multiplicative Noise — shares topic coverage
- Oblateness Effects on Solar Sail in the Restricted Three–body Problem — shares topic coverage
Article metrics
Real usage data collected on this platform.
37
Page views
0
PDF downloads
3
Outbound clicks
2
Citations
Views over time
Views by country
Approximate, from request IP at view time — not citizenship or institution. Countries with fewer than 5 views are grouped as "Other".
Traffic sources
Referring site, by host.
Views and downloads exclude known bots/crawlers. Citations combines this platform's own DOI-resolved index with each external source's own reported total — see Cited by above for individually listed citing works. Last refreshed 0 seconds ago.