Symbolic dynamics and relaxation oscillations

DOI10.1016/0167-2789(80)90014-7zbMath1194.37018OpenAlexW1963689859MaRDI QIDQ994978

John Guckenheimer

Publication date: 13 September 2010

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

Full work available at URL: https://doi.org/10.1016/0167-2789(80)90014-7

Mathematics Subject Classification ID

Nonlinear dynamics in mechanics (70K99) Symbolic dynamics (37B10)

Related Items (10)

Transition to topological chaos for circle maps ⋮ Phase locking, period doubling bifurcations and chaos in a mathematical model of a periodically driven oscillator: A theory for the entrainment of biological oscillators and the generation of cardiac dysrhythmias ⋮ A new randomness-generating mechanism in forced relaxation oscillations ⋮ Correlation functions of an autonomous stochastic system with time delays ⋮ On the arithmetic of phase locking: coupled neurons as a lattice on \(\mathbb{R}^{2}\) ⋮ The mathematical modeling of entrained biological oscillators ⋮ Global bifurcations of a periodically forced nonlinear oscillator ⋮ Singular perturbations and a mapping on an interval for the forced van der Pol relaxation oscillator ⋮ Nonlinear dynamics of the heartbeat. II: Subharmonic bifurcations of the cardiac interbeat interval in sinus node disease ⋮ Symbolic dynamics of the cubic map

Cites Work

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• The abundance of wild hyperbolic sets and non-smooth stable sets for diffeomorphisms
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• On Non-Linear Differential Equations of the Second Order: I. the Equation y¨ − k (1-y ² )y˙ + y = b λk cos(λl + α), k Large
• Equilibrium states and the ergodic theory of Anosov diffeomorphisms
• A second order differential equation with singular solutions

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