AN ATLAS OF ROBUST, STABLE, HIGH-DIMENSIONAL LIMIT CYCLES

DOI10.1142/S0218127409025225zbMath1183.34043OpenAlexW2022818603MaRDI QIDQ5306404

Roy Robust, Leon Glass

Publication date: 9 April 2010

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218127409025225

zbMATH Keywords

hypercubeinverse problemHopf bifurcationhomoclinic bifurcationpiecewise linear equations

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation theory for ordinary differential equations (34C23) Directed graphs (digraphs), tournaments (05C20) Systems biology, networks (92C42)

Related Items (6)

A modelling framework for gene regulatory networks including transcription and translation ⋮ Chaotic dynamics and diffusion in a piecewise linear equation ⋮ Hybrid models of genetic networks: mathematical challenges and biological relevance ⋮ Dynamics in piecewise linear and continuous models of complex switching networks ⋮ A SPECTRAL RADIUS ESTIMATE AND ENTROPY OF HYPERCUBES ⋮ Quasi-potential calculation and minimum action method for limit cycle

Uses Software

• AUTO
• AUTO-07P

Cites Work

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• A methodological basis for description and analysis of systems with complex switch-like interactions
• Analysis and generic properties of gene regulatory networks with graded response functions
• Diagonal stability of a class of cyclic systems and its connection with the secant criterion
• Combinatorial explosion in model gene networks
• Periodic solutions in systems of piecewise- linear differential equations
• An Algebraic Algorithm for the Identification of Glass Networks with Periodic Orbits Along Cyclic Attractors
• Evolving complex dynamics in electronic models of genetic networks

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