Discontinuity-induced bifurcation cascades in flows and maps with application to models of the yeast cell cycle

DOI10.1016/j.physd.2013.12.011zbMath1283.92020OpenAlexW1991996813MaRDI QIDQ2442604

Mike R. Jeffrey, Harry J. Dankowicz

Publication date: 4 April 2014

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

Full work available at URL: https://research-information.bris.ac.uk/en/publications/77b4bfdc-0459-4d9c-ab10-48142619c07e

zbMATH Keywords

cell divisionsaddle-node bifurcationsgrazing bifurcationsperiod-adding sequencesborder collisions

Mathematics Subject Classification ID

Dynamical systems in biology (37N25) Cell biology (92C37) Qualitative investigation and simulation of ordinary differential equation models (34C60)

Related Items (5)

Periods 1 + 2 imply chaos in steep or nonsmooth maps ⋮ Oscillations and multiple equilibria in microvascular blood flow ⋮ Analysis of atypical orbits in one-dimensional piecewise-linear discontinuous maps ⋮ The hidden unstable orbits of maps with gaps ⋮ Bifurcations of hidden orbits in discontinuous maps

Uses Software

• COCO

Cites Work

• Scaling law in saddle-node bifurcations for one-dimensional maps: a complex variable approach
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• CALCULATION OF BIFURCATION CURVES BY MAP REPLACEMENT
• The dynamics of a simplified pinball machine
• Sufficient conditions for a period incrementing big bang bifurcation in one-dimensional maps
• Chaotic Behavior in Piecewise Continuous Difference Equations
• The Order of Appearance of Oscillation Modes of a Piecewise Linear Map
• Recipes for Continuation
• Bifurcation phenomena in two-dimensional piecewise smooth discontinuous maps
• The anharmonic route to chaos: kneading theory
• Dynamics of a piecewise linear map with a gap

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