Universality and self-similarity in the bifurcations of circle maps

DOI10.1016/0167-2789(85)90055-7zbMath0593.58030OpenAlexW1970957000MaRDI QIDQ1076390

Leon Glass, Jacques Bélair

Publication date: 1985

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-2789(85)90055-7

zbMATH Keywords

Circle mapsglobal bifurcations of circle mapsphysical and biological systems

Mathematics Subject Classification ID

Applications of dynamical systems (37N99) Iteration of real functions in one variable (26A18) Local and nonlocal bifurcation theory for dynamical systems (37G99)

Related Items (19)

Bifurcations in a Periodically Stimulated Limit Cycle Oscillator with Finite Relaxation Times ⋮ Transition to topological chaos for circle maps ⋮ A genealogy for the periodic orbits of a class of 1D maps ⋮ On difference equations motivated by modelling the heart ⋮ Coexistence of triple, quadruple attractors and Wada basin boundaries in a predator-prey model with additional food for predators ⋮ Chaos, noise, and extinction in models of population growth ⋮ Symbolic dynamics and characterization of complexity ⋮ Quasiperiodic resonance and bifurcations of tori in the weakly nonlinear Duffing oscillator ⋮ Cardiac arrhythmias and circle maps−A classical problem ⋮ Some flesh on the skeleton: the bifurcation structure of bimodal maps ⋮ Torsion-adding and asymptotic winding number for periodic window sequences ⋮ A realistic, minimal ``middle layer for neural networks ⋮ An asymmetrical phase locking structure for a non-excitable cell model ⋮ Symbolic dynamics and skeletons of circle maps ⋮ A circle map in a human heart ⋮ Symbolic dynamics and systematics of periodic windows ⋮ Termination of reentry by infra- and supra-threshold pulses ⋮ Composite families of maps ⋮ Global bifurcations of a periodically forced nonlinear oscillator

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