LINEAR AND NONLINEAR ARABESQUES: A STUDY OF CLOSED CHAINS OF NEGATIVE 2-ELEMENT CIRCUITS

DOI10.1142/S0218127413300334zbMath1277.34058arXiv1302.1071OpenAlexW3098007931MaRDI QIDQ2866048

Jacques Demongeot, Vasileios Basios, René Thomas, Pasquale Nardone, Chris G. Antonopoulos

Publication date: 13 December 2013

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

Full work available at URL: https://arxiv.org/abs/1302.1071

zbMATH Keywords

Lyapunov exponentsconservative systemsarabesque systemsJacobian circuits and frontierssmaller alignment index (SALI)

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Nonlinear ordinary differential equations and systems (34A34) Stability of solutions to ordinary differential equations (34D20) Linear ordinary differential equations and systems (34A30) Characteristic and Lyapunov exponents of ordinary differential equations (34D08) Analytic circuit theory (94C05) Qualitative investigation and simulation of ordinary differential equation models (34C60) Invariant manifolds for ordinary differential equations (34C45)

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Cites Work

• Unnamed Item
• Combinatorics of Boolean automata circuits dynamics
• Stable periodicity and negative circuits in differential systems
• Robustness in biological regulatory networks. I: Mathematical approach
• Liénard systems and potential-Hamiltonian decomposition. I: Methodology
• Geometrical properties of local dynamics in Hamiltonian systems: the generalized alignment index (GALI) method
• Dynamics of positive automata networks
• Lyapunov characteristic exponents for smooth dynamical systems and for Hamiltonian systems; a method for computing all of them. I: Theory
• On limit cycles of monotone functions with symmetric connection graph
• Detection of ordered and chaotic motion using the dynamical spectra
• Local negative circuits and fixed points in non-expansive Boolean networks
• Necessary Conditions for Multistationarity and Stable Periodicity
• Multistationarity, the basis of cell differentiation and memory. I. Structural conditions of multistationarity and other nontrivial behavior
• A FURTHER UNDERSTANDING OF PHASE SPACE PARTITION DIAGRAMS
• CHARACTERISTIC LYAPUNOV EXPONENTS AND SMOOTH ERGODIC THEORY
• Alignment indices: a new, simple method for determining the ordered or chaotic nature of orbits
• CHAOTIC DYNAMICS OF N-DEGREE OF FREEDOM HAMILTONIAN SYSTEMS
• DETERMINISTIC CHAOS SEEN IN TERMS OF FEEDBACK CIRCUITS: ANALYSIS, SYNTHESIS, "LABYRINTH CHAOS"
• FRONTIER DIAGRAMS: PARTITION OF PHASE SPACE ACCORDING TO THE SIGNS OF EIGENVALUES OR SIGN PATTERNS OF THE CIRCUITS

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